The 300-meter radiotelescope in Arecibo, Puerto Rico (Fig.

A properly exposed photograph is taken at 16 and What lens opening is required if the shutter speed is

A television camera lens has a 17-cm focal length and a lens diameter of 6.0 cm. What is its f- number?

A 65-mm-focal-length lens has f-stops ranging from 1.4 to 22. What is the corresponding range of lens diaphragm diameters?

A light meter reports that a camera setting of at 5.6 will give a correct exposure. But the photographer wishes to use 11 to increase the depth of field. What should the shutter speed be?

For a camera equipped with a 55-mm-focal-length lens, what is the object distance if the image height equals the object height? How far is the object from the image on the film?

A nature photographer wishes to shoot a 34-m-tall tree from a distance of 65 m. What focal-length lens should be used if the image is to fill the 24-mm height of the sensor?

A 200-mm-focal-length lens can be adjusted so that it is 200.0 mm to 208.2 mm from the film. For what range of object distances can it be adjusted?

How large is the image of the Sun on film used in a camera with (a) a 28-mm-focal-length lens, (b) a 50-mmfocal-length lens, and (c) a 135-mm-focal-length lens? (d) If the 50-mm lens is considered normal for this camera, what relative magnification does each of the other two lenses provide? The Sun has diameter and it is 1.5 * 108 kmaway.

If a 135-mm telephoto lens is designed to cover object distances from 1.30 m to over what distance must the lens move relative to the plane of the sensor or film?

Show that for objects very far away (assume infinity), the magnification of any camera lens is proportional to its focal length.

(I) A human eyeball is about 2.0 cm long and the pupil has a maximum diameter of about 8.0 mm. What is the “speed” of this lens?

A person struggles to read by holding a book at arms length, a distance of 52 cm away. What power of reading glasses should be prescribed for her, assuming they will be placed 2.0 cm from the eye and she wants to read at the normal near point of 25 cm?

Reading glasses of what power are needed for a person whose near point is 125 cm, so that he can read a computer screen at 55 cm? Assume a lenseye distance of 1.8 cm.

(II) An eye is corrected by a –5.50-D lens, 2.0 cm from the eye. (a) Is this eye near- or farsighted? (b) What is this eye’s far point without glasses?

A persons right eye can see objects clearly only if they are between 25 cm and 85 cm away. (a) What power of contact lens is required so that objects far away are sharp? (b) What will be the near point with the lens in place?

About how much longer is the nearsighted eye in Example 256 than the 2.0 cm of a normal eye?

A person has a far point of 14 cm. What power glasses would correct this vision if the glasses were placed 2.0 cm from the eye? What power contact lenses, placed on the eye, would the person need?

One lens of a nearsighted persons eyeglasses has a focal length of and the lens is 1.8 cm from the eye. If the person switches to contact lenses placed directly on the eye, what should be the focal length of the corresponding contact lens?

(II) What is the focal length of the eye–lens system when viewing an object (a) at infinity, and (b) 34 cm from the eye? Assume that the lens–retina distance is 2.0 cm.

(III) The closely packed cones in the fovea of the eye have a diameter of about \(2 \mu \mathrm{m}\). For the eye to discern two images on the fovea as distinct, assume that the images must be separated by at least one cone that is not excited. If these images are of two point-like objects at the eye’s 25-cm near point, how far apart are these barely resolvable objects? Assume the eye’s diameter (cornea-to-fovea distance) is 2.0 cm. Equation Transcription: Text Transcription: 2 \mu m

A nearsighted person has near and far points of 10.6 and 20.0 cm, respectively. If she puts on contact lenses with power what are her new near and far points?

What is the focal length of a magnifying glass of 3.2x magnification for a relaxed normal eye?

What is the magnification of a lens used with a relaxed eye if its focal length is 16 cm?

A magnifier is rated at for a normal eye focusing on an image at the near point. (a) What is its focal length? (b) What is its focal length if the refers to a relaxed eye?

Sherlock Holmes is using an 8.20-cm-focal-length lens as his magnifying glass. To obtain maximum magnification, where must the object be placed (assume a normal eye), and what will be the magnification?

A small insect is placed 4.85 cm from a -focallength lens. Calculate (a) the position of the image, and (b) the angular magnification.

A 3.80-mm-wide bolt is viewed with a 9.60-cm-focallength lens. A normal eye views the image at its near point. Calculate (a) the angular magnification, (b) the width of the image, and (c) the object distance from the lens.

A magnifying glass with a focal length of 9.2 cm is used to read print placed at a distance of 8.0 cm. Calculate (a) the position of the image; (b) the angular magnification.

A writer uses a converging lens of focal length as a magnifying glass to read fine print on his book contract. Initially, the writer holds the lens above the fine print so that its image is at infinity. To get a better look, he then moves the lens so that the image is at his 25-cm near point. How far, and in what direction (toward or away from the fine print) did the writer move the lens? Assume his eye is adjusted to remain always very near the magnifying glass.

A magnifying glass is rated at for a normal eye that is relaxed. What would be the magnification for a relaxed eye whose near point is (a) 75 cm, and (b) 15 cm? Explain the differences.

What is the magnification of an astronomical telescope whose objective lens has a focal length of 82 cm, and whose eyepiece has a focal length of 2.8 cm? What is the overall length of the telescope when adjusted for a relaxed eye?

The overall magnification of an astronomical telescope is desired to be . If an objective of 88-cm focal length is used, what must be the focal length of the eyepiece? What is the overall length of the telescope when adjusted for use by the relaxed eye?

A binocular has 3.5-cm-focal-length eyepieces. What is the focal length of the objective lenses?

An astronomical telescope has an objective with focal length 75 cm and a eyepiece. What is the total magnification?

An astronomical telescope has its two lenses spaced 82.0 cm apart. If the objective lens has a focal length of 78.5 cm, what is the magnification of this telescope? Assume a relaxed eye.

A Galilean telescope adjusted for a relaxed eye is 36.8 cm long. If the objective lens has a focal length of 39.0 cm, what is the magnification?

What is the magnifying power of an astronomical telescope using a reflecting mirror whose radius of curvature is 6.1 m and an eyepiece whose focal length is 2.8 cm?

The Moons image appears to be magnified by a reflecting astronomical telescope with an eyepiece having a focal length of 3.1 cm. What are the focal length and radius of curvature of the main (objective) mirror?

A astronomical telescope is adjusted for a relaxed eye when the two lenses are 1.10 m apart. What is the focal length of each lens?

An astronomical telescope longer than about 50 cm is not easy to hold by hand. Estimate the maximum angular magnification achievable for a telescope designed to be handheld. Assume its eyepiece lens, if used as a magnifying glass, provides a magnification of for a relaxed eye with near point N = 25 cm

(III) A reflecting telescope (Fig. 25–22b) has a radius of curvature of 3.00 m for its objective mirror and a radius of curvature of -1.50 m for its eyepiece mirror. If the distance between the two mirrors is 0.90 m, how far in front of the eyepiece should you place the electronic sensor to record the image of a star?

A pair of binoculars has an objective focal length of 26 cm. If the binoculars are focused on an object 4.0 m away (from the objective), what is the magnification? (The refers to objects at infinity; Eq. 253 holds only for objects at infinity and not for nearby ones.)

(I) A microscope uses an eyepiece with a focal length of 1.70 cm. Using a normal eye with a final image at infinity, the barrel length is 17.5 cm and the focal length of the objective lens is 0.65 cm.What is the magnification of the microscope?

A microscope uses a 0.40-cm-focal-length objective lens. If the barrel length is 17.5 cm, what is the focal length of the eyepiece? Assume a normal eye and that the final image is at infinity

A 17-cm-long microscope has an eyepiece with a focal length of 2.5 cm and an objective with a focal length of 0.33 cm. What is the approximate magnification?

A microscope has a eyepiece and a objective lens 20.0 cm apart. Calculate (a) the total magnification, (b) the focal length of each lens, and (c) where the object must be for a normal relaxed eye to see it in focus.

Repeat Problem 46 assuming that the final image is located 25 cm from the eyepiece (near point of a normal eye)

A microscope has a 1.8-cm-focal-length eyepiece and a 0.80-cm objective. Assuming a relaxed normal eye, calculate (a) the position of the object if the distance between the lenses is 14.8 cm, and (b) the total magnification.

The eyepiece of a compound microscope has a focal length of 2.80 cm and the objective lens has If an object is placed 0.790 cm from the objective lens, calculate (a) the distance between the lenses when the microscope is adjusted for a relaxed eye, and (b) the total magnification

An inexpensive instructional lab microscope allows the user to select its objective lens to have a focal length of 32 mm, 15 mm, or 3.9 mm. It also has two possible eyepieces with magnifications and Each objective forms a real image 160 mm beyond its focal point. What are the largest and smallest overall magnifications obtainable with this instrument?

An achromatic lens is made of two very thin lenses, placed in contact, that have focal lengths and (a) Is the combination converging or diverging? (b) What is the net focal length?

A planoconvex lens (Fig. 2331a) has one flat surface and the other has This lens is used to view a red and yellow object which is 66.0 cm away from the lens. The index of refraction of the glass is 1.5106 for red light and 1.5226 for yellow light. What are the locations of the red and yellow images formed by the lens? [Hint: See Section 2310.]

(I) What is the angular resolution limit (degrees) set by diffraction for the 100-inch (254-cm mirror diameter) Mt.Wilson telescope \((\lambda = 560\ nm)\)?

What is the resolving power of a microscope with a 5-mm-diameter objective which has = 9 mm?

Two stars 18 light-years away are barely resolved by a 66-cm (mirror diameter) telescope. How far apart are the stars? Assume and that the resolution is limited by diffraction

The nearest neighboring star to the Sun is about 4 lightyears away. If a planet happened to be orbiting this star at an orbital radius equal to that of the EarthSun distance, what minimum diameter would an Earth-based telescopes aperture have to be in order to obtain an image that resolved this starplanet system? Assume the light emitted by the star and planet has a wavelength of 550 nm

If you could shine a very powerful flashlight beam toward the Moon, estimate the diameter of the beam when it reaches the Moon. Assume that the beam leaves the flashlight through a 5.0-cm aperture, that its white light has an average wavelength of 550 nm, and that the beam spreads due to diffraction only.

The normal lens on a 35-mm camera has a focal length of 50.0 mm. Its aperture diameter varies from a maximum of 25 mm ( 2) to a minimum of 3.0 mm ( 16). Determine the resolution limit set by diffraction for ( 2) and ( 16). Specify as the number of lines per millimeter resolved on the detector or film. Take

Suppose that you wish to construct a telescope that can resolve features 6.5 km across on the Moon, 384,000 km away. You have a 2.0-m-focal-length objective lens whose diameter is 11.0 cm. What focal-length eyepiece is needed if your eye can resolve objects 0.10 mm apart at a distance of 25 cm? What is the resolution limit set by the size of the objective lens (that is, by diffraction)?

X-rays of wavelength 0.138 nm fall on a crystal whose atoms, lying in planes, are spaced 0.285 nm apart. At what angle (relative to the surface, Fig. 2538) must the X-rays be directed if the first diffraction maximum is to be observed?

First-order Bragg diffraction is observed at 23.8 relative to the crystal surface, with spacing between atoms of 0.24 nm. (a) At what angle will second order be observed? (b) What is the wavelength of the X-rays?

If X-ray diffraction peaks corresponding to the first three orders ( and 3) are measured, can both the X-ray wavelength and lattice spacing d be determined? Prove your answer.

(a) Suppose for a conventional X-ray image that the X-ray beam consists of parallel rays. What would be the magnification of the image? (b) Suppose, instead, that the X-rays come from a point source (as in Fig. 2541) that is 15 cm in front of a human body which is 25 cm thick, and the film is pressed against the persons back. Determine and discuss the range of magnifications that result

A pinhole camera uses a tiny pinhole instead of a lens. Show, using ray diagrams, how reasonably sharp images can be formed using such a pinhole camera. In particular, consider two point objects 2.0 cm apart that are 1.0 m from a 1.0-mm-diameter pinhole. Show that on a piece of film 7.0 cm behind the pinhole the two objects produce two separate circles that do not overlap

Suppose that a correct exposure is at 11. Under the same conditions, what exposure time would be needed for a pinhole camera (Problem 64) if the pinhole diameter is 1.0 mm and the film is 7.0 cm from the hole?

An astronomical telescope has a magnification of If the two lenses are 28 cm apart, determine the focal length of each lens.

(a) How far away can a human eye distinguish two car headlights 2.0 m apart? Consider only diffraction effects and assume an eye pupil diameter of 6.0 mm and a wavelength of 560 nm. (b) What is the minimum angular separation an eye could resolve when viewing two stars, considering only diffraction effects? In reality, it is about of arc. Why is it not equal to your answer in (b)?

Figure 2548 was taken from the NIST Laboratory (National Institute of Standards and Technology) in Boulder, CO, 2.0 km from the hiker in the photo. The Suns image was 15 mm across on the film. Estimate the focal length of the camera lens (actually a telescope). The Sun has diameter and it is away.

A 1.0-cm-diameter lens with a focal length of 35 cm uses blue light to image two objects 15 m away that are very close together. What is the closest those objects can be to each other and still be imaged as separate objects?

A movie star catches a reporter shooting pictures of her at home. She claims the reporter was trespassing. To prove her point, she gives as evidence the film she seized. Her 1.65-m height is 8.25 mm high on the film, and the focal length of the camera lens was 220 mm. How far away from the subject was the reporter standing?

As early morning passed toward midday, and the sunlight got more intense, a photographer noted that, if she kept her shutter speed constant, she had to change the f-number from 5.6 to 16. By what factor had the sunlight intensity increased during that time?

A child has a near point of 15 cm. What is the maximum magnification the child can obtain using a 9.5-cm-focallength magnifier? What magnification can a normal eye obtain with the same lens? Which person sees more detail?

A woman can see clearly with her right eye only when objects are between 45 cm and 135 cm away. Prescription bifocals should have what powers so that she can see distant objects clearly (upper part) and be able to read a book 25 cm away (lower part) with her right eye? Assume that the glasses will be 2.0 cm from the eye.

What is the magnifying power of a lens used as a magnifier? Assume a relaxed normal eye.

A physicist lost in the mountains tries to make a telescope using the lenses from his reading glasses. They have powers of and respectively. (a) What maximum magnification telescope is possible? (b) Which lens should be used as the eyepiece?

A person with normal vision adjusts a microscope for a good image when her eye is relaxed. She then places a camera where her eye was. For what object distance should the camera be set? Explain

A 50-year-old man uses lenses to read a newspaper 25 cm away. Ten years later, he must hold the paper 38 cm away to see clearly with the same lenses. What power lenses does he need now in order to hold the paper 25 cm away? (Distances are measured from the lens.)

Two converging lenses, one with and the other with are made into a telescope. (a) What are the length and magnification? Which lens should be the eyepiece? (b) Assume these lenses are now combined to make a microscope; if the magnification needs to be how long would the microscope be?

An X-ray tube operates at 95 kV with a current of 25 mA and nearly all the electron energy goes into heat. If the specific heat of the 0.065-kg anode plate is what will be the temperature rise per minute if no cooling water is used? (See Fig. 2536.)

Human vision normally covers an angle of roughly 40° horizontally. A “normal” camera lens then is defined as follows:When focused on a distant horizontal object which subtends an angle of \(40^{\circ}\), the lens produces an image that extends across the full horizontal extent of the camera’s light-recording medium (film or electronic sensor). Determine the focal length f of the “normal” lens for the following types of cameras: (a) a 35-mm camera that records images on film 36 mm wide; (b) a digital camera that records images on a charge-coupled device (CCD) 1.60 cm wide.

The objective lens and the eyepiece of a telescope are spaced 85 cm apart. If the eyepiece is what is the total magnification of the telescope?

. Sam purchases eyeglasses which correct his faulty vision to put his near point at 25 cm. (Assume he wears the lenses 2.0 cm from his eyes.) Calculate (a) the focal length of Sams glasses, (b) Sams near point without glasses. (c) Pam, who has normal eyes with near point at 25 cm, puts on Sams glasses. Calculate Pams near point with Sams glasses on

Spy planes fly at extremely high altitudes (25 km) to avoid interception. If their cameras are to discern features as small as 5 cm, what is the minimum aperture of the camera lens to afford this resolution? (Use ) l = 580 nm

X-rays of wavelength 0.0973 nm are directed at an unknown crystal. The second diffraction maximum is recorded when the X-rays are directed at an angle of 21.2 relative to the crystal surface. What is the spacing between crystal planes?

The Hubble Space Telescope, with an objective diameter of 2.4 m, is viewing the Moon. Estimate the minimum distance between two objects on the Moon that the Hubble can distinguish. Consider diffraction of light with wavelength 550 nm. Assume the Hubble is near the Earth.

The Earth and Moon are separated by about When Mars is from Earth, could a person standing on Mars resolve the Earth and its Moon as two separate objects without a telescope? Assume a pupil diameter of 5 mm and

You want to design a spy satellite to photograph license plate numbers. Assuming it is necessary to resolve points separated by 5 cm with 550-nm light, and that the satellite orbits at a height of 130 km, what minimum lens aperture (diameter) is required?

Given two 12-cm-focal-length lenses, you attempt to make a crude microscope using them. While holding these lenses a distance 55 cm apart, you position your microscope so that its objective lens is distance from a small object. Assume your eyes near point (a) For your microscope to function properly, what should be? (b) Assuming your eye is relaxed when using it, what magnification M does your microscope achieve? (c) Since the length of your microscope is not much greater than the focal lengths of its lenses, the approximation is not valid. If you apply this approximation to your microscope, what % error do you make in your microscopes true magnification?

The power of one lens in a pair of eyeglasses is The radius of curvature of the outside surface is 16.0 cm. What is the radius of curvature of the inside surface? The lens is made of plastic with n = 1.62.

Problem 1COQ Because of diffraction, a light microscope has a useful magnification of about (a) 50x; (b) 100x; (c) 500x; (d) 2000x; (e) 500x; and the smallest objects it can resolve have a size of about (a) 10 nm; (b) 100 nm; (c) 500 nm; (d) 2500 nm; (e) 5500 nm.

Problem 1MCQ The image of a nearby object formed by a camera lens is (a) at the lens’ focal point. (b) always blurred. (c) at the same location as the image of an object at infinity. (d) farther from the lens than the lens’ focal point.

\((I)\) A properly exposed photograph is taken at \(f / 16 \text { and } \frac{1}{100} s\). What lens opening is required if the shutter speed is \(\frac{1}{400} s\)? Equation Transcription: Text Transcription: (I) f/16 and 1 100s 1 400s

Problem 1Q Why must a camera lens be moved farther from the sensor or film to focus on a closer object?

Problem 1SL Digital cameras may offer an optical zoom or a digital zoom. An optical zoom uses a variable focal-length lens, so only the central part of the field of view fills the entire sensor; a digital zoom electronically includes only the central pixels of the sensor, so objects are larger in the final picture. Discuss which is better, and why

Problem 2MCQ What is a megapixel in a digital camera? (a) A large spot on the detector where the image is focused. (b) A special kind of lens that gives a sharper image. (c) A number related to how many photographs the camera can store. (d) A million light-sensitive spots on the detector. (e) A number related to how fast the camera can take pictures.

Problem 2Q Why is the depth of field greater, and the image sharper, when a camera lens is “stopped down” to a larger f-number? Ignore diffraction.

Problem 2P (I) A television camera lens has a 17-cm focal length and a lens diameter of 6.0 cm. What is itsf-number?

Problem 2SL Which of the following statements is true? (See Section 25–2.) Write a brief explanation why each is true or false. (a) Contact lenses and eyeglasses for the same person would have the same power. (b) Farsighted people can see far clearly but not near. (c) Nearsighted people cannot see near or far clearly. (d) Astigmatism in vision is corrected by using different spherical lenses for each eye.

Problem 3MCQ When a nearsighted person looks at a distant object through her glasses, the image produced by the glasses should be (a) about 25 cm from her eye. (b) at her eye’s far point. (c) at her eye’s near point. (d) at the far point for a normal eye.

Problem 3P (I) A 65-mm-focal-length lens has f-stops ranging from f/1.4 to f/22. What is the corresponding range of lens diaphragm diameters?

Problem 3Q Redo Examples 25–3 and 25–4 assuming the sensor has only 6MP. Explain the different results and their impact on finished photographs.

Problem 3SL Redo Examples 25–3 and 25–4 assuming the sensor has only 6MP. Explain the different results and their impact on finished photographs.

If the distance from your eye’s lens to the retina is shorter than for a normal eye, you will struggle to see objects that are (a) nearby. (b) far away. (c) colorful. (d) moving fast.

\(\text { (I) }\) A light meter reports that a camera setting of \(\frac{1}{500} s \text { at } f / 5.6\) will give a correct exposure. But the photographer wishes to use \(f / 11\) to increase the depth of field. What should the shutter speed be? Equation Transcription: Text Transcription: (I) 1 500s at f/5.6 f/11

Problem 4Q Why are bifocals needed mainly by older persons and not generally by younger people?

Problem 4SL Describe at least four advantages of using mirrors rather than lenses for an astronomical telescope.

Problem 5MCQ The image produced on the retina of the eye is _____ compared to the object being viewed. (a) inverted. (c) sideways. (b) upright. (d) enlarged.

Problem 5P (II) For a camera equipped with a 55-mm-focal-length lens, what is the object distance if the image height equals the object height? How far is the object from the image on the film?

Will a nearsighted person who wears corrective lenses in her glasses be able to see clearly underwater when wearing those glasses? Use a diagram to show why or why not.

Problem 5SL An astronomical telescope, Fig. 25–20, produces an inverted image. One way to make a telescope that produces an upright image is to insert a third lens between the objective and the eyepiece, Fig. 25–23b. To have the same magnification, the non-inverting telescope will be longer. Suppose lenses of focal length 150 cm, 1.5 cm, and 10 cm are available. Where should these three lenses be placed to make a non-inverting telescope with magnification 100 X?

How do eyeglasses help a nearsighted person see more clearly? (a) Diverging lenses bend light entering the eye, so the image focuses farther from the front of the eye. (b) Diverging lenses bend light entering the eye, so the image focuses closer to the front of the eye. (c) Converging lenses bend light entering the eye, so the image focuses farther from the front of the eye. (d) Converging lenses bend light entering the eye, so the image focuses closer to the front of the eye. (e) Lenses adjust the distance from the cornea to the back of the eye.

Problem 6P (II) A nature photographer wishes to shoot a 34-m-tall tree from a distance of 65 m. What focal-length lens should be used if the image is to fill the 24-mm height of the sensor?

You can tell whether people are nearsighted or farsighted by looking at the width of their face through their glasses. If a person’s face appears narrower through the glasses (Fig. 25–47), is the person farsighted or nearsighted? Try to explain, but also check experimentally with friends who wear glasses.

Mizar, the second star from the end of the Big Dipper's handle, appears to have a companion star, Alcor. From Earth, Mizar and Alcor have an angular separation of 12 arc minutes (1 arc min \(=\frac{1}{60}\) of \(1^{\circ}\)). Using Examples 25-10 and 25-11, estimate the angular resolution of the human eye (in arc min). From your estimate, explain if these two stars can be resolved by the naked eye.

When you closely examine an object through a magnifying glass, the magnifying glass (a) makes the object bigger. (b) makes the object appear closer than it actually is. (c) makes the object appear farther than it actually is. (d) causes additional light rays to be emitted by the object.

Problem 7P (II) A 200-mm-focal-length lens can be adjusted so that it is 200.0 mm to 208.2 mm from the film. For what range of object distances can it be adjusted?

Problem 7Q In attempting to discern distant details, people will sometimes squint. Why does this help?

Problem 8MCQ It would be impossible to build a microscope that could use visible light to see the molecular structure of a crystal because. (a) lenses with enough magnification cannot be made. (b) lenses cannot be ground with fine enough precision. (c) lenses cannot be placed in the correct place with enough precision. (d) diffraction limits the resolving power to about the size of the wavelength of the light used. (e) More than one of the above is correct.

Problem 8P (II) How large is the image of the Sun on film used in a camera with (a) a 28-mm-focal-length lens, (b) a 50-mmfocal- length lens, and (c) a 135-mm-focal-length lens? (d) If the 50-mm lens is considered normal for this camera, what relative magnification does each of the other two lenses provide? The Sun has diameter 1.4 X 106 km, and it is 1.5 X 108 km away away.

Problem 8Q Is the image formed on the retina of the human eye upright or inverted? Discuss the implications of this for our perception of objects.

Problem 9MCQ Why aren’t white-light microscopes made with a magnification of 3000 X? (a) Lenses can’t be made large enough. (b) Lenses can’t be made small enough. (c) Lenses can’t be made with short enough focal lengths. (d) Lenses can’t be made with long enough focal lengths. (e) Diffraction limits useful magnification to several times less than this.

(II) If a 135-mm telephoto lens is designed to cover object distances from 1.30 m to \(\infty\), over what distance must the lens move relative to the plane of the sensor or film?

Problem 9Q The human eye is much like a camera—yet, when a camera shutter is left open and the camera is moved, the image will be blurred. But when you move your head with your eyes open, you still see clearly. Explain.

Problem 10MCQ The resolving power of a microscope is greatest when the object being observed is illuminated by (a) ultraviolet light. (c) visible light. (b) infrared light. (d) radio waves.

Problem 10P (III) Show that for objects very far away (assume infinity), the magnification of any camera lens is proportional to its focal length.

Problem 10Q Reading glasses use converging lenses. A simple magnifier is also a converging lens. Are reading glasses therefore magnifiers? Discuss the similarities and differences between converging lenses as used for these two different purposes.

Problem 11MCQ Which of the following statements is true? (a) A larger-diameter lens can better resolve two distant points. (b) Red light can better resolve two distant points than blue light can. (c) It is easier to resolve distant objects than nearer objects. (d) Objects that are closer together are easier to resolve than objects that are farther apart.

Problem 11P (I) A human eyeball is about 2.0 cm long and the pupil has a maximum diameter of about 8.0 mm. What is the “speed” of this lens?

Problem 11Q Nearsighted people often look over (or under) their glasses when they want to see something small up close, like a cell phone screen. Why?

Problem 12MCQ While you are photographing a dog, it begins to move away. What must you do to keep it in focus? (a) Increase the f-stop value. (b) Decrease the f-stop value. (c) Move the lens away from the sensor or film. (d)Move the lens closer to the sensor or film. (e) None of the above.

Problem 12P (II) A person struggles to read by holding a book at arm’s length, a distance of 52 cm away. What power of reading glasses should be prescribed for her, assuming they will be placed 2.0 cm from the eye and she wants to read at the “normal” near point of 25 cm?

Problem 12Q Spherical aberration in a thin lens is minimized if rays are bent equally by the two surfaces. If a planoconvex lens is used to form a real image of an object at infinity, which surface should face the object? Use ray diagrams to show why.

Problem 13MCQ A converging lens, like the type used in a magnifying glass, (a) always produces a magnified image (image taller than the object). (b) can also produce an image smaller than the object. (c) always produces an upright image. (d) can also produce an inverted image (upside down). (e) None of these statements are true.

Problem 13P (II) Reading glasses of what power are needed for a person whose near point is 125 cm, so that he can read a computer screen at 55 cm? Assume a lens–eye distance of 1.8 cm.

Problem 13Q Explain why chromatic aberration occurs for thin lenses but not for mirrors.

Problem 14P (II) An eye is corrected by a -5.50-D lens, 2.0 cm from the eye. (a) Is this eye near- or farsighted? (b) What is this eye’s far point without glasses?

Problem 14Q Inexpensive microscopes for children’s use usually produce images that are colored at the edges. Why?

Problem 15P (II) A person’s right eye can see objects clearly only if they are between 25 cm and 85 cm away. (a) What power of contact lens is required so that objects far away are sharp? (b) What will be the near point with the lens in place?

Problem 15Q Which aberrations present in a simple lens are not present (or are greatly reduced) in the human eye?

(II) About how much longer is the nearsighted eye in Example 25–6 than the 2.0 cm of a normal eye?

By what factor can you improve resolution, other things being equal, if you use blue light \((\lambda=450 \mathrm{~nm})\) rather than red (700 nm)? Equation Transcription: Text Transcription: (\lambda=450 nm)

Problem 17P (II) A person has a far point of 14 cm. What power glasses would correct this vision if the glasses were placed 2.0 cm from the eye? What power contact lenses, placed on the eye, would the person need?

Atoms have diameters of about \(10^{-8} \mathrm{~cm}\). Can visible light be used to “see” an atom? Explain. Equation Transcription: Text Transcription: 10^-8 cm

Problem 18P (II) One lens of a nearsighted person’s eyeglasses has a focal length of -26.0 cm and the lens is 1.8 cm from the eye. If the person switches to contact lenses placed directly on the eye, what should be the focal length of the corresponding contact lens?

Which color of visible light would give the best resolution in a microscope? Explain.

Problem 19P (II) What is the focal length of the eye–lens system when viewing an object (a) at infinity, and (b) 34 cm from the eye? Assume that the lens–retina distance is 2.0 cm.

Problem 19Q For both converging and diverging lenses, discuss how the focal length for red light differs from that for violet light.

Problem 20P (III) The closely packed cones in the fovea of the eye have a diameter of about 2µm. For the eye to discern two images on the fovea as distinct, assume that the images must be separated by at least one cone that is not excited. If these images are of two point-like objects at the eye’s 25-cm near point, how far apart are these barely resolvable objects? Assume the eye’s diameter (cornea-to-fovea distance) is 2.0 cm.

The \(300 \text { - meter }\) radiotelescope in Arecibo, Puerto Rico (Fig. 25–33), is the world’s largest radiotelescope, but many other radiotelescopes are also very large. Why are radiotelescopes so big? Why not make optical telescopes that are equally large? (The largest optical telescopes have diameters of about \(10 \text { meters }\).) Equation Transcription: Text Transcription: 300-meter 10 meters

The 300-meter radiotelescope in Arecibo, Puerto Rico (Fig. 25–33), is the world’s largest radiotelescope, but many other radiotelescopes are also very large. Why are radiotelescopes so big? Why not make optical telescopes that are equally large? (The largest optical telescopes have diameters of about 10 meters.)

(III) A nearsighted person has near and far points of 10.6 and 20.0 cm, respectively. If she puts on contact lenses with power P = –4.00 D, what are her new near and far points?

Problem 23P (I) What is the magnification of a lens used with a relaxed eye if its focal length is 16 cm?

Problem 24P (I) A magnifier is rated at 3.5 X for a normal eye focusing on an image at the near point. (a) What is its focal length? (b) What is its focal length if the 3.5 X refers to a relaxed eye?

If the lens of Example 25–1 is \(50.4 \mathrm{~mm}\) from the film or sensor, what is the object distance for sharp focus? Equation Transcription: Text Transcription: 50.4 mm

The criterion of 0.030 mm as the diameter of a circle of confusion as acceptable sharpness is how many dots per mm on the sensor?

What power of contact lens is needed for an eye to see distant objects if its far point is 25 cm?

A 40 \times telescope has a 1.2-cm focal length eyepiece. What is the focal length of the objective lens?

Problem 25EE Someone claims a spy satellite camera can see 3-cm-high newspaper headlines from an altitude of 100 km. If diffraction were the only limitation use Eq. 25–7 to determine what diameter lens the camera would have.

Return to the Chapter-Opening Question, page 713, and answer it again now. Try to explain why you may have answered differently the first time.

Problem 25P (II) Sherlock Holmes is using an 8.20-cm-focal-length lens as his magnifying glass. To obtain maximum magnification, where must the object be placed (assume a normal eye), and what will be the magnification?

Problem 25P (II) Sherlock Holmes is using an 8.20-cm-focal-length lens as his magnifying glass. To obtain maximum magnification, where must the object be placed (assume a normal eye), and what will be the magnification?

Problem 26P (II) A small insect is placed 4.85 cm from a +5.00-cm –focal-length lens. Calculate (a) the position of the image, and (b) the angular magnification.

Problem 27P (II) A 3.80-mm-wide bolt is viewed with a 9.60-cm-focallength lens. A normal eye views the image at its near point. Calculate (a) the angular magnification, (b) the width of the image, and (c) the object distance from the lens.

Problem 28P (II) A magnifying glass with a focal length of 9.2 cm is used to read print placed at a distance of 8.0 cm. Calculate (a) the position of the image; (b) the angular magnification.

Problem 29P (III) A writer uses a converging lens of focal length F =12 cm as a magnifying glass to read fine print on his book contract. Initially, the writer holds the lens above the fine print so that its image is at infinity. To get a better look, he then moves the lens so that the image is at his 25-cm near point. How far, and in what direction (toward or away from the fine print) did the writer move the lens? Assume his eye is adjusted to remain always very near the magnifying glass

Problem 30P (III) A magnifying glass is rated at 3.0 X for a normal eye that is relaxed. What would be the magnification for a relaxed eye whose near point is (a) 75 cm, and (b) 15 cm? Explain the differences.

(I) What is the magnification of an astronomical telescope whose objective lens has a focal length of 82 cm, and whose eyepiece has a focal length of 2.8 cm? What is the overall length of the telescope when adjusted for a relaxed eye?

Problem 32P (I) The overall magnification of an astronomical telescope is desired to be 25X . If an objective of 88-cm focal length is used, what must be the focal length of the eyepiece? What is the overall length of the telescope when adjusted for use by the relaxed eye?

Problem 33P (II) A 7.0 X binocular has 3.5-cm-focal-length eyepieces. What is the focal length of the objective lenses?

Problem 34P (II) An astronomical telescope has an objective with focal length 75 cm and a +25 -D eyepiece. What is the total magnification?

Problem 35P (II) An astronomical telescope has its two lenses spaced 82.0 cm apart. If the objective lens has a focal length of 78.5 cm, what is the magnification of this telescope? Assume a relaxed eye.

Problem 36P (II) A Galilean telescope adjusted for a relaxed eye is 36.8 cm long. If the objective lens has a focal length of 39.0 cm, what is the magnification?

Problem 37P (II) What is the magnifying power of an astronomical telescope using a reflecting mirror whose radius of curvature is 6.1 m and an eyepiece whose focal length is 2.8 cm?

(II) The Moon’s image appears to be magnified 150 \(\times\) by a reflecting astronomical telescope with an eyepiece having a focal length of 3.1 cm. What are the focal length and radius of curvature of the main (objective) mirror?

Problem 39P (II) A 120 X astronomical telescope is adjusted for a relaxed eye when the two lenses are 1.10 m apart. What is the focal length of each lens?

Problem 40P (II) An astronomical telescope longer than about 50 cm is not easy to hold by hand. Estimate the maximum angular magnification achievable for a telescope designed to be handheld. Assume its eyepiece lens, if used as a magnifying glass, provides a magnification of 5X for a relaxed eye with near point N = 25 cm

Problem 41P (III) A reflecting telescope (Fig. 25–22b) has a radius of curvature of 3.00 m for its objective mirror and a radius of curvature of -1.50 m for its eyepiece mirror. If the distance between the two mirrors is 0.90 m, how far in front of the eyepiece should you place the electronic sensor to record the image of a star?

Problem 42P (III) A 6. 5 X pair of binoculars has an objective focal length of 26 cm. If the binoculars are focused on an object 4.0 m away (from the objective), what is the magnification? (The 6. 5 X refers to objects at infinity; Eq. 25–3 holds only for objects at infinity and not for nearby ones.)

Problem 43P (I) A microscope uses an eyepiece with a focal length of 1.70 cm. Using a normal eye with a final image at infinity, the barrel length is 17.5 cm and the focal length of the objective lens is 0.65 cm. What is the magnification of the microscope?

Problem 44P (I) A 720 X microscope uses a 0.40-cm-focal-length objective lens. If the barrel length is 17.5 cm, what is the focal length of the eyepiece? Assume a normal eye and that the final image is at infinity.

Problem 45P (I) A 17-cm-long microscope has an eyepiece with a focal length of 2.5 cm and an objective with a focal length of 0.33 cm. What is the approximate magnification?

Problem 46P (II) A microscope has a 14.0 X eyepiece and a 60.0 X objective lens 20.0 cm apart. Calculate (a) the total magnification, (b) the focal length of each lens, and (c) where the object must be for a normal relaxed eye to see it in focus.

Problem 47P (II) Repeat Problem 46 assuming that the final image is located 25 cm from the eyepiece (near point of a normal eye).

Problem 48P (II) A microscope has a 1.8-cm-focal-length eyepiece and a 0.80-cm objective. Assuming a relaxed normal eye, calculate (a) the position of the object if the distance between the lenses is 14.8 cm, and (b) the total magnification.

Problem 49P (II) The eyepiece of a compound microscope has a focal length of 2.80 cm and the objective lens has f =0.740 cm If an object is placed 0.790 cm from the objective lens, calculate (a) the distance between the lenses when the microscope is adjusted for a relaxed eye, and (b) the total magnification.

Problem 50P (III) An inexpensive instructional lab microscope allows the user to select its objective lens to have a focal length of 32 mm, 15 mm, or 3.9 mm. It also has two possible eyepieces with magnifications 5X and 15 X Each objective forms a real image 160 mm beyond its focal point. What are the largest and smallest overall magnifications obtainable with this instrument?

Problem 51P (II) An achromatic lens is made of two very thin lenses, placed in contact, that have focal lengths f1 = -27.8 cm and f2 = +25.3 cm. (a) Is the combination converging or diverging? (b) What is the net focal length?

Problem 52P (III) A planoconvex lens (Fig. 23–31a) has one flat surface and the other has R =14.5 cm. This lens is used to view a red and yellow object which is 66.0 cm away from the lens. The index of refraction of the glass is 1.5106 for red light and 1.5226 for yellow light. What are the locations of the red and yellow images formed by the lens? [Hint: See Section 23–10.]

Problem 53P (I) What is the angular resolution limit (degrees) set by diffraction for the 100-inch (254-cm mirror diameter) Mt. Wilson telescope (? = 560 nm)?

Problem 54P (I) What is the resolving power of a microscope (? =550 nm) with a 5-mm-diameter objective which has f =9mm?

Problem 55P (II) Two stars 18 light-years away are barely resolved by a 66-cm (mirror diameter) telescope. How far apart are the stars? Assume ? =550 nm and that the resolution is limited by diffraction.

Problem 56P (II) The nearest neighboring star to the Sun is about 4 light-years away. If a planet happened to be orbiting this star at an orbital radius equal to that of the Earth–Sun distance, what minimum diameter would an Earth-based telescope’s aperture have to be in order to obtain an image that resolved this star–planet system? Assume the light emitted by the star and planet has a wavelength of 550 nm.

Problem 57P (II) If you could shine a very powerful flashlight beam toward the Moon, estimate the diameter of the beam when it reaches the Moon. Assume that the beam leaves the flashlight through a 5.0-cm aperture, that its white light has an average wavelength of 550 nm, and that the beam spreads due to diffraction only.

Problem 58P (II) The normal lens on a 35-mm camera has a focal length of 50.0 mm. Its aperture diameter varies from a maximum of 25 mm ( 2) to a minimum of 3.0 mm ( 16). Determine the resolution limit set by diffraction for ( 2) and ( 16). Specify as the number of lines per millimeter resolved on the detector or film. Take ? =560 nm

Problem 59P (III) Suppose that you wish to construct a telescope that can resolve features 6.5 km across on the Moon, 384,000 km away. You have a 2.0-m-focal-length objective lens whose diameter is 11.0 cm. What focal-length eyepiece is needed if your eye can resolve objects 0.10 mm apart at a distance of 25 cm? What is the resolution limit set by the size of the objective lens (that is, by diffraction)? ? =560 nm.

Problem 60P (II) X-rays of wavelength 0.138 nm fall on a crystal whose atoms, lying in planes, are spaced 0.285 nm apart. At what angle (relative to the surface, Fig. 25–38) must the X-rays be directed if the first diffraction maximum is to be observed?

Problem 61P (II) First-order Bragg diffraction is observed at 23.8° relative to the crystal surface, with spacing between atoms of 0.24 nm. (a) At what angle will second order be observed? (b) What is the wavelength of the X-rays?

(II) If X-ray diffraction peaks corresponding to the first three orders (m = 1, 2, and 3) are measured, can both the X-ray wavelength \(\lambda\) and lattice spacing d be determined? Prove your answer.

Problem 63P (II) (a) Suppose for a conventional X-ray image that the X-ray beam consists of parallel rays. What would be the magnification of the image? (b) Suppose, instead, that the X-rays come from a point source (as in Fig. 25–41) that is 15 cm in front of a human body which is 25 cm thick, and the film is pressed against the person’s back. Determine and discuss the range of magnifications that result.

Problem 64P A pinhole camera uses a tiny pinhole instead of a lens. Show, using ray diagrams, how reasonably sharp images can be formed using such a pinhole camera. In particular, consider two point objects 2.0 cm apart that are 1.0 m from a 1.0-mm-diameter pinhole. Show that on a piece of film 7.0 cm behind the pinhole the two objects produce two separate circles that do not overlap.

Suppose that a correct exposure is \(\frac{1}{250} s \text { at } f / 11\). Under the same conditions, what exposure time would be needed for a pinhole camera (Problem 64 ) if the pinhole diameter is \(1.0 \mathrm{~mm}\) and the film is \(7.0 \mathrm{~cm}\) from the hole? Equation Transcription: Text Transcription: 1 250 s at f/11 1.0 mm and 7.0 cm

An astronomical telescope has a magnification of \(7.5 \times\). If the two lenses are 28 cm apart, determine the focal length of each lens.

Problem 67GP (a) How far away can a human eye distinguish two car headlights 2.0 m apart? Consider only diffraction effects and assume an eye pupil diameter of 6.0 mm and a wavelength of 560 nm. (b) What is the minimum angular separation an eye could resolve when viewing two stars, considering only diffraction effects? In reality, it is about 1 of arc. Why is it not equal to your answer in (b)?

Figure 25-48 was taken from the NIST Laboratory (National Institute of Standards and Technology) in Boulder, CO, \(2.0 \mathrm{~km}\) from the hiker in the photo. The Sun's image was \(15 \mathrm{~mm}\) across on the film. Estimate the focal length of the camera lens (actually a telescope). The Sun has diameter \(1.4 x 10^{6} \mathrm{~km}\), and it is \(1.5 x 10^{8} \mathrm{~km}\) away. Equation Transcription: Text Transcription: 2.0 km 15 mm 1.4 x 10^6km 1.5 x 10^8km

Problem 69GP A 1.0-cm-diameter lens with a focal length of 35 cm uses blue light to image two objects 15 m away that are very close together. What is the closest those objects can be to each other and still be imaged as separate objects?

Problem 70GP A movie star catches a reporter shooting pictures of her at home. She claims the reporter was trespassing. To prove her point, she gives as evidence the film she seized. Her 1.65-m height is 8.25 mm high on the film, and the focal length of the camera lens was 220 mm. How far away from the subject was the reporter standing?

Problem 71GP As early morning passed toward midday, and the sunlight got more intense, a photographer noted that, if she kept her shutter speed constant, she had to change the f-number from f/5.6 to f/16. By what factor had the sunlight intensity increased during that time?

Problem 72GP A child has a near point of 15 cm. What is the maximum magnification the child can obtain using a 9.5-cm-focallength magnifier? What magnification can a normal eye obtain with the same lens?Which person sees more detail?

Problem 73GP A woman can see clearly with her right eye only when objects are between 45 cm and 135 cm away. Prescription bifocals should have what powers so that she can see distant objects clearly (upper part) and be able to read a book 25 cm away (lower part) with her right eye? Assume that the glasses will be 2.0 cm from the eye.

Problem 74GP What is the magnifying power of a lens used as a +4.0-D magnifier? Assume a relaxed normal eye.

A physicist lost in the mountains tries to make a telescope using the lenses from his reading glasses. They have powers of +2.0 D and +5.5 D, respectively. (a) What maximum magnification telescope is possible? (b) Which lens should be used as the eyepiece?

Problem 76GP A person with normal vision adjusts a microscope for a good image when her eye is relaxed. She then places a camera where her eye was. For what object distance should the camera be set? Explain.

Problem 77GP A 50-year-old man uses +2.5 D lenses to read a newspaper 25 cm away. Ten years later, he must hold the paper 38 cm away to see clearly with the same lenses. What power lenses does he need now in order to hold the paper 25 cm away? (Distances are measured from the lens.)

Problem 78GP Two converging lenses, one with f=4.0 cm and the other with f=48 cm are made into a telescope. (a) What are the length and magnification? Which lens should be the eyepiece? (b) Assume these lenses are now combined to make a microscope; if the magnification needs to be 25x how long would the microscope be?

An X-ray tube operates at 95 kV with a current of 25 mA and nearly all the electron energy goes into heat. If the specific heat of the 0.065-kg anode plate is \(0.11 \mathrm{kcal} / \mathrm{kg} \cdot \mathrm{C}^{\circ}\), what will be the temperature rise per minute if no cooling water is used? (See Fig. 25–36.) Equation Transcription: ° Text Transcription: 0.11 kcal / kg \cdot {C}^{\circ}

Problem 80GP Human vision normally covers an angle of roughly 40° horizontally. A “normal” camera lens then is defined as follows:When focused on a distant horizontal object which subtends an angle of 40°, the lens produces an image that extends across the full horizontal extent of the camera’s light-recording medium (film or electronic sensor). Determine the focal length f of the “normal” lens for the following types of cameras: (a) a 35-mm camera that records images on film 36 mm wide; (b) a digital camera that records images on a charge-coupled device (CCD) 1.60 cm wide.

The objective lens and the eyepiece of a telescope are spaced 85 cm apart. If the eyepiece is +19 D, what is the total magnification of the telescope?

Problem 82GP Sam purchases +3.50-D eyeglasses which correct his faulty vision to put his near point at 25 cm. (Assume he wears the lenses 2.0 cm from his eyes.) Calculate (a) the focal length of Sam’s glasses, (b) Sam’s near point without glasses. (c) Pam, who has normal eyes with near point at 25 cm, puts on Sam’s glasses. Calculate Pam’s near point with Sam’s glasses on.

Spy planes fly at extremely high altitudes \((25 \mathrm{~km})\) to avoid interception. If their cameras are to discern features as small as \(5 \mathrm{~cm}\), what is the minimum aperture of the camera lens to afford this resolution? (Use \(\lambda=580 \mathrm{~nm}\). ) Equation Transcription: Text Transcription: (25 km) 5 cm \lambda=580 nm

Problem 84GP X-rays of wavelength 0.0973 nm are directed at an unknown crystal. The second diffraction maximum is recorded when the X-rays are directed at an angle of 21.2° relative to the crystal surface.What is the spacing between crystal planes?

Problem 85GP The Hubble Space Telescope, with an objective diameter of 2.4 m, is viewing the Moon. Estimate the minimum distance between two objects on the Moon that the Hubble can distinguish. Consider diffraction of light with wavelength 550 nm. Assume the Hubble is near the Earth.

Problem 86GP The Earth and Moon are separated by about 400 x 106 m. When Mars is 8 x 1010 m from Earth, could a person standing on Mars resolve the Earth and its Moon as two separate objects without a telescope? Assume a pupil diameter of 5 mm and ? = 550 m.

You want to design a spy satellite to photograph license plate numbers. Assuming it is necessary to resolve points separated by 5 cm with 550-nm light, and that the satellite orbits at a height of 130 km, what minimum lens aperture (diameter) is required?

Given two 12-cm-focal-length lenses, you attempt to make a crude microscope using them.While holding these lenses a distance 55 cm apart, you position your microscope so that its objective lens is distance \(d_0\) from a small object. Assume your eye’s near point N = 25 cm. (a) For your microscope to function properly, what should \(d_0\) be? (b) Assuming your eye is relaxed when using it, what magnification M does your microscope achieve? (c) Since the length of your microscope is not much greater than the focal lengths of its lenses, the approximation \(M \approx N \ell/f_ef_o\) is not valid. If you apply this approximation to your microscope, what % error do you make in your microscope’s true magnification?

Problem 89GP The power of one lens in a pair of eyeglasses is -3.5 D. The radius of curvature of the outside surface is 16.0 cm. What is the radius of curvature of the inside surface? The lens is made of plastic with n = 1.62.

A properly exposed photograph is taken at 16 and What lens opening is required if the shutter speed is

A television camera lens has a 17-cm focal length and a lens diameter of 6.0 cm. What is its f-number?

A 65-mm-focal-length lens has f-stops ranging from 1.4 to 22. What is the corresponding range of lens diaphragm diameters?

A light meter reports that a camera setting of at 5.6 will give a correct exposure. But the photographer wishes to use 11 to increase the depth of field. What should the shutter speed be?

For a camera equipped with a 55-mm-focal-length lens, what is the object distance if the image height equals the object height? How far is the object from the image on the film?

A nature photographer wishes to shoot a 34-m-tall tree from a distance of 65 m. What focal-length lens should be used if the image is to fill the 24-mm height of the sensor?

A 200-mm-focal-length lens can be adjusted so that it is 200.0 mm to 208.2 mm from the film. For what range of object distances can it be adjusted?

How large is the image of the Sun on film used in a camera with (a) a 28-mm-focal-length lens, (b) a 50-mmfocal-length lens, and (c) a 135-mm-focal-length lens? (d) If the 50-mm lens is considered normal for this camera, what relative magnification does each of the other two lenses provide? The Sun has diameter and it is 1.5 * 108 kmaway.

If a 135-mm telephoto lens is designed to cover object distances from 1.30 m to over what distance must the lens move relative to the plane of the sensor or film?

Show that for objects very far away (assume infinity), the magnification of any camera lens is proportional to its focal length.

A human eyeball is about 2.0 cm long and the pupil has a maximum diameter of about 8.0 mm. What is the speed of this lens?

A person struggles to read by holding a book at arms length, a distance of 52 cm away. What power of reading glasses should be prescribed for her, assuming they will be placed 2.0 cm from the eye and she wants to read at the normal near point of 25 cm?

Reading glasses of what power are needed for a person whose near point is 125 cm, so that he can read a computer screen at 55 cm? Assume a lenseye distance of 1.8 cm.

An eye is corrected by a lens, 2.0 cm from the eye. (a) Is this eye near- or farsighted? (b) What is this eyes far point without glasses?

A persons right eye can see objects clearly only if they are between 25 cm and 85 cm away. (a) What power of contact lens is required so that objects far away are sharp? (b) What will be the near point with the lens in place?

About how much longer is the nearsighted eye in Example 256 than the 2.0 cm of a normal eye?

A person has a far point of 14 cm. What power glasses would correct this vision if the glasses were placed 2.0 cm from the eye? What power contact lenses, placed on the eye, would the person need?

One lens of a nearsighted persons eyeglasses has a focal length of and the lens is 1.8 cm from the eye. If the person switches to contact lenses placed directly on the eye, what should be the focal length of the corresponding contact lens?

What is the focal length of the eyelens system when viewing an object (a) at infinity, and (b) 34 cm from the eye? Assume that the lensretina distance is 2.0 cm

The closely packed cones in the fovea of the eye have a diameter of about For the eye to discern two images on the fovea as distinct, assume that the images must be separated by at least one cone that is not excited. If these images are of two point-like objects at the eyes 25-cm near point, how far apart are these barely resolvable objects? Assume the eyes diameter (cornea-to-fovea distance) is 2.0 cm.

A nearsighted person has near and far points of 10.6 and 20.0 cm, respectively. If she puts on contact lenses with power what are her new near and far points?

What is the focal length of a magnifying glass of 3.2x magnification for a relaxed normal eye?

What is the magnification of a lens used with a relaxed eye if its focal length is 16 cm?

A magnifier is rated at for a normal eye focusing on an image at the near point. (a) What is its focal length? (b) What is its focal length if the refers to a relaxed eye?

(II) Sherlock Holmes is using an 8.20-cm-focal-length lens as his magnifying glass. To obtain maximum magnification, where must the object be placed (assume a normal eye), and what will be the magnification?

A small insect is placed 4.85 cm from a -focallength lens. Calculate (a) the position of the image, and (b) the angular magnification.

A 3.80-mm-wide bolt is viewed with a 9.60-cm-focallength lens. A normal eye views the image at its near point. Calculate (a) the angular magnification, (b) the width of the image, and (c) the object distance from the lens.

A magnifying glass with a focal length of 9.2 cm is used to read print placed at a distance of 8.0 cm. Calculate (a) the position of the image; (b) the angular magnification.

(III) A writer uses a converging lens of focal length f = 12 cm as a magnifying glass to read fine print on his book contract. Initially, the writer holds the lens above the fine print so that its image is at infinity. To get a better look, he then moves the lens so that the image is at his 25-cm near point. How far, and in what direction (toward or away from the fine print) did the writer move the lens? Assume his eye is adjusted to remain always very near the magnifying glass.

A magnifying glass is rated at for a normal eye that is relaxed. What would be the magnification for a relaxed eye whose near point is (a) 75 cm, and (b) 15 cm? Explain the differences.

What is the magnification of an astronomical telescope whose objective lens has a focal length of 82 cm, and whose eyepiece has a focal length of 2.8 cm? What is the overall length of the telescope when adjusted for a relaxed eye?

The overall magnification of an astronomical telescope is desired to be . If an objective of 88-cm focal length is used, what must be the focal length of the eyepiece? What is the overall length of the telescope when adjusted for use by the relaxed eye?

A binocular has 3.5-cm-focal-length eyepieces. What is the focal length of the objective lenses?

An astronomical telescope has an objective with focal length 75 cm and a eyepiece. What is the total magnification?

An astronomical telescope has its two lenses spaced 82.0 cm apart. If the objective lens has a focal length of 78.5 cm, what is the magnification of this telescope? Assume a relaxed eye.

A Galilean telescope adjusted for a relaxed eye is 36.8 cm long. If the objective lens has a focal length of 39.0 cm, what is the magnification?

What is the magnifying power of an astronomical telescope using a reflecting mirror whose radius of curvature is 6.1 m and an eyepiece whose focal length is 2.8 cm?

(II) The Moon’s image appears to be magnified 150X by a reflecting astronomical telescope with an eyepiece having a focal length of 3.1 cm. What are the focal length and radius of curvature of the main (objective) mirror?

A astronomical telescope is adjusted for a relaxed eye when the two lenses are 1.10 m apart. What is the focal length of each lens?

An astronomical telescope longer than about 50 cm is not easy to hold by hand. Estimate the maximum angular magnification achievable for a telescope designed to be handheld. Assume its eyepiece lens, if used as a magnifying glass, provides a magnification of for a relaxed eye with near point N = 25 cm

A reflecting telescope (Fig. 2522b) has a radius of curvature of 3.00 m for its objective mirror and a radius of curvature of for its eyepiece mirror. If the distance between the two mirrors is 0.90 m, how far in front of the eyepiece should you place the electronic sensor to record the image of a star?

A pair of binoculars has an objective focal length of 26 cm. If the binoculars are focused on an object 4.0 m away (from the objective), what is the magnification? (The refers to objects at infinity; Eq. 253 holds only for objects at infinity and not for nearby ones.)

A microscope uses an eyepiece with a focal length of 1.70 cm. Using a normal eye with a final image at infinity, the barrel length is 17.5 cm and the focal length of the objective lens is 0.65 cm. What is the magnification of the microscope?

A microscope uses a 0.40-cm-focal-length objective lens. If the barrel length is 17.5 cm, what is the focal length of the eyepiece? Assume a normal eye and that the final image is at infinity

(I) A 17-cm-long microscope has an eyepiece with a focal length of 2.5 cm and an objective with a focal length of 0.33 cm. What is the approximate magnification?

A microscope has a eyepiece and a objective lens 20.0 cm apart. Calculate (a) the total magnification, (b) the focal length of each lens, and (c) where the object must be for a normal relaxed eye to see it in focus.

(II) Repeat Problem 46 assuming that the final image is located 25 cm from the eyepiece (near point of a normal eye).

A microscope has a 1.8-cm-focal-length eyepiece and a 0.80-cm objective. Assuming a relaxed normal eye, calculate (a) the position of the object if the distance between the lenses is 14.8 cm, and (b) the total magnification.

The eyepiece of a compound microscope has a focal length of 2.80 cm and the objective lens has If an object is placed 0.790 cm from the objective lens, calculate (a) the distance between the lenses when the microscope is adjusted for a relaxed eye, and (b) the total magnification

(III) An inexpensive instructional lab microscope allows the user to select its objective lens to have a focal length of 32 mm, 15 mm, or 3.9 mm. It also has two possible eyepieces with magnifications 5X and 15X. Each objective forms a real image 160 mm beyond its focal point. What are the largest and smallest overall magnifications obtainable with this instrument?

(II) An achromatic lens is made of two very thin lenses, placed in contact, that have focal lengths \(f_{1}=-27.8 \mathrm{~cm}\) and \(f2 = ±25.3 cmf_{2}=+25.3 \mathrm{~cm}\) (a) Is the combination converging or diverging? (b) What is the net focal length? Equation Transcription: Text Transcription: f_1=–27.8 cm f_2=+25.3 cm

A planoconvex lens (Fig. 2331a) has one flat surface and the other has This lens is used to view a red and yellow object which is 66.0 cm away from the lens. The index of refraction of the glass is 1.5106 for red light and 1.5226 for yellow light. What are the locations of the red and yellow images formed by the lens? [Hint: See Section 2310.]

(I) What is the angular resolution limit (degrees) set by diffraction for the 100-inch (254-cm mirror diameter) Mt. Wilson telescope \((\lambda=560 \mathrm{~nm})\)? Equation Transcription: Text Transcription: (\lambda=560 nm)

(I) What is the resolving power of a microscope \((\lambda=550 \mathrm{~nm})\) with a 5-mm-diameter objective which has f = 9 mm? Equation Transcription: Text Transcription: (\lambda=550 nm)

(II) Two stars 18 light-years away are barely resolved by a 66-cm (mirror diameter) telescope. How far apart are the stars? Assume \(\lambda=550 \mathrm{~nm}\) and that the resolution is limited by diffraction. Equation Transcription: Text Transcription: \lambda=550 nm

The nearest neighboring star to the Sun is about 4 lightyears away. If a planet happened to be orbiting this star at an orbital radius equal to that of the EarthSun distance, what minimum diameter would an Earth-based telescopes aperture have to be in order to obtain an image that resolved this starplanet system? Assume the light emitted by the star and planet has a wavelength of 550 nm

If you could shine a very powerful flashlight beam toward the Moon, estimate the diameter of the beam when it reaches the Moon. Assume that the beam leaves the flashlight through a 5.0-cm aperture, that its white light has an average wavelength of 550 nm, and that the beam spreads due to diffraction only.

(II) The normal lens on a 35-mm camera has a focal length of 50.0 mm. Its aperture diameter varies from a maximum of 25 mm (f/2) to a minimum of 3.0 mm (f/16). Determine the resolution limit set by diffraction for (f/2) and (f/16). Specify as the number of lines per millimeter resolved on the detector or film. Take \(\lambda=560 \mathrm{~nm}\). Equation Transcription: Text Transcription: \lambda=560 nm

(III) Suppose that you wish to construct a telescope that can resolve features 6.5 km across on the Moon, 384,000 km away. You have a 2.0-m-focal-length objective lens whose diameter is 11.0 cm. What focal-length eyepiece is needed if your eye can resolve objects 0.10 mm apart at a distance of 25 cm? What is the resolution limit set by the size of the objective lens (that is, by diffraction)? Use \(\lambda=560 \mathrm{~nm}\). Equation Transcription: Text Transcription: \lambda=560 nm

(II) X-rays of wavelength 0.138 nm fall on a crystal whose atoms, lying in planes, are spaced 0.285 nm apart. At what angle \(\phi\) (relative to the surface, Fig. 25–38) must the X-rays be directed if the first diffraction maximum is to be observed?

First-order Bragg diffraction is observed at 23.8 relative to the crystal surface, with spacing between atoms of 0.24 nm. (a) At what angle will second order be observed? (b) What is the wavelength of the X-rays?

(II) If X-ray diffraction peaks corresponding to the first three orders (m = 1, 2, and 3) are measured, can both the X-ray wavelength \(\lambda\) and lattice spacing d be determined? Prove your answer. Equation Transcription: Text Transcription: \lambda

(a) Suppose for a conventional X-ray image that the X-ray beam consists of parallel rays. What would be the magnification of the image? (b) Suppose, instead, that the X-rays come from a point source (as in Fig. 25–41) that is 15 cm in front of a human body which is 25 cm thick, and the film is pressed against the person’s back. Determine and discuss the range of magnifications that result.

A pinhole camera uses a tiny pinhole instead of a lens. Show, using ray diagrams, how reasonably sharp images can be formed using such a pinhole camera. In particular, consider two point objects 2.0 cm apart that are 1.0 m from a 1.0-mm-diameter pinhole. Show that on a piece of film 7.0 cm behind the pinhole the two objects produce two separate circles that do not overlap

Suppose that a correct exposure is at 11. Under the same conditions, what exposure time would be needed for a pinhole camera (Problem 64) if the pinhole diameter is 1.0 mm and the film is 7.0 cm from the hole?

An astronomical telescope has a magnification of \(7.5 \times\). If the two lenses are 28 cm apart, determine the focal length of each lens.

(a) How far away can a human eye distinguish two car headlights 2.0 m apart? Consider only diffraction effects and assume an eye pupil diameter of 6.0 mm and a wavelength of 560 nm. (b) What is the minimum angular separation an eye could resolve when viewing two stars, considering only diffraction effects? In reality, it is about 1’ of arc. Why is it not equal to your answer in (b)?

Figure 2548 was taken from the NIST Laboratory (National Institute of Standards and Technology) in Boulder, CO, 2.0 km from the hiker in the photo. The Suns image was 15 mm across on the film. Estimate the focal length of the camera lens (actually a telescope). The Sun has diameter and it is away.

A 1.0-cm-diameter lens with a focal length of 35 cm uses blue light to image two objects 15 m away that are very close together. What is the closest those objects can be to each other and still be imaged as separate objects?

A movie star catches a reporter shooting pictures of her at home. She claims the reporter was trespassing. To prove her point, she gives as evidence the film she seized. Her 1.65-m height is 8.25 mm high on the film, and the focal length of the camera lens was 220 mm. How far away from the subject was the reporter standing?

As early morning passed toward midday, and the sunlight got more intense, a photographer noted that, if she kept her shutter speed constant, she had to change the f-number from 5.6 to 16. By what factor had the sunlight intensity increased during that time?

A child has a near point of 15 cm. What is the maximum magnification the child can obtain using a 9.5-cm-focallength magnifier? What magnification can a normal eye obtain with the same lens? Which person sees more detail?

A woman can see clearly with her right eye only when objects are between 45 cm and 135 cm away. Prescription bifocals should have what powers so that she can see distant objects clearly (upper part) and be able to read a book 25 cm away (lower part) with her right eye? Assume that the glasses will be 2.0 cm from the eye.

What is the magnifying power of a +4.0-D lens used as a magnifier? Assume a relaxed normal eye.

A physicist lost in the mountains tries to make a telescope using the lenses from his reading glasses. They have powers of and respectively. (a) What maximum magnification telescope is possible? (b) Which lens should be used as the eyepiece?

A person with normal vision adjusts a microscope for a good image when her eye is relaxed. She then places a camera where her eye was. For what object distance should the camera be set? Explain

A 50-year-old man uses lenses to read a newspaper 25 cm away. Ten years later, he must hold the paper 38 cm away to see clearly with the same lenses. What power lenses does he need now in order to hold the paper 25 cm away? (Distances are measured from the lens.)

Two converging lenses, one with and the other with are made into a telescope. (a) What are the length and magnification? Which lens should be the eyepiece? (b) Assume these lenses are now combined to make a microscope; if the magnification needs to be how long would the microscope be?

An X-ray tube operates at 95 kV with a current of 25 mA and nearly all the electron energy goes into heat. If the specific heat of the 0.065-kg anode plate is what will be the temperature rise per minute if no cooling water is used? (See Fig. 2536.)

Human vision normally covers an angle of roughly 40 horizontally. A normal camera lens then is defined as follows: When focused on a distant horizontal object which subtends an angle of 40, the lens produces an image that extends across the full horizontal extent of the cameras light-recording medium (film or electronic sensor). Determine the focal length f of the normal lens for the following types of cameras: (a) a 35-mm camera that records images on film 36 mm wide; (b) a digital camera that records images on a charge-coupled device (CCD) 1.60 cm wide.

The objective lens and the eyepiece of a telescope are spaced 85 cm apart. If the eyepiece is what is the total magnification of the telescope?

. Sam purchases eyeglasses which correct his faulty vision to put his near point at 25 cm. (Assume he wears the lenses 2.0 cm from his eyes.) Calculate (a) the focal length of Sams glasses, (b) Sams near point without glasses. (c) Pam, who has normal eyes with near point at 25 cm, puts on Sams glasses. Calculate Pams near point with Sams glasses on

Spy planes fly at extremely high altitudes (25 km) to avoid interception. If their cameras are to discern features as small as 5 cm, what is the minimum aperture of the camera lens to afford this resolution? (Use ) l = 580 nm

X-rays of wavelength 0.0973 nm are directed at an unknown crystal. The second diffraction maximum is recorded when the X-rays are directed at an angle of 21.2 relative to the crystal surface. What is the spacing between crystal planes?

The Hubble Space Telescope, with an objective diameter of 2.4 m, is viewing the Moon. Estimate the minimum distance between two objects on the Moon that the Hubble can distinguish. Consider diffraction of light with wavelength 550 nm. Assume the Hubble is near the Earth.

The Earth and Moon are separated by about \(400 \times 10^{6} \mathrm{~m}\). When Mars is \(8 \times 10^{10} \mathrm{~m}\) from Earth, could a person standing on Mars resolve the Earth and its Moon as two separate objects without a telescope? Assume a pupil diameter of 5 mm and \(\lambda=550 \mathrm{~m}\). Equation Transcription: Text Transcription: 400 x 10^6 m 8 x 10^10 m \lambda=550m

You want to design a spy satellite to photograph license plate numbers. Assuming it is necessary to resolve points separated by 5 cm with 550-nm light, and that the satellite orbits at a height of 130 km, what minimum lens aperture (diameter) is required?

Given two 12-cm-focal-length lenses, you attempt to make a crude microscope using them. While holding these lenses a distance 55 cm apart, you position your microscope so that its objective lens is distance from a small object. Assume your eyes near point (a) For your microscope to function properly, what should be? (b) Assuming your eye is relaxed when using it, what magnification M does your microscope achieve? (c) Since the length of your microscope is not much greater than the focal lengths of its lenses, the approximation is not valid. If you apply this approximation to your microscope, what % error do you make in your microscopes true magnification?

The power of one lens in a pair of eyeglasses is The radius of curvature of the outside surface is 16.0 cm. What is the radius of curvature of the inside surface? The lens is made of plastic with n = 1.62.