A friend lends you the eyepiece of his microscope to use onyour own microscope. He

On a sunny summer day, wilh the sun overhead, you can stand under a tree and look on the ground at the pattern of light that has passed through gaps between the leaves. You may see illuminated circles of varying brightness. Why are there circles, when the gaps between the leaves have irregular shapes?

Suppose you have two pinhole cameras. The first has a small round hole in the front of the camera. The second is identical in every regard, except that it has a square hole of' the same area as the round hole in the first camera. Would the pictures taken by these two cameras, under the same conditions, be different in any obvious way? Explain.

A photographer focuses his camera on his subject. The subject then moves closer to the camera. To refocus, should the lens be moved closer to or farther from the de tector? Explai n.

The object for a magnifier is usua lly placed very close to the focal point of the lens, creating a vittual image very far away where it can be viewed with the relaxed eye. But the object could be placed so that the image is at the eye's near-point distance. In this case, the image can be viewed only by using the full accommodation of the eye. When used this way, is the angular magni fication greater than, equal to, or less than the magnification when the image is far away? Explain.

A nature photographer taking a close-up shot of an insect replaces the standard lens on his camera with a lens that has a shotter focal length and is positioned farther from the CCD detector. Explain why he does this.

The CCD detector in a certain camera has a width of 8 mm. The photographer realizes that with the lens she is currently using, she can't tit the entire landscape she is trying lo photograph into her picture. Should she swi tch to a lens with a longer or shorter focal length? Explain.

All humans have what is known as a blind spot, where the optic nerve exits the eye and no light-sensitive cells exist. To locate your blind spot, look at the figure of the cross. Close your left eye and place your index finger on the cross. Slowly move your finger to the le ft while following it with your right eye. At a certain point the cross wi ll disappear. Is your right eye's blind spot on the right or left side of your retina? Explain.

Suppose you wanted special glasses designed to wear underwater, without a face mask. Should the glasses use a converging or diverging lens in order for you to be able to focus under water? Explai n.

You have lenses with the following focal lengths: f = 25 mm, 50 mm, I 00 mm, and 200 mm. Which lens or pair of lenses would you use, and in what arrangement, to get the highestpower magnifier, microscope, and telescope? Explain.

An 8-year-old chi ld and a 75-year-old man both use the same magnifier to observe a bug. For whom does the magnifier more likely have the higher magnification? Explain.

A friend lends you the eyepiece of his microscope to use on your own microscope. He claims that since his eyepiece has the same diameter as yours but twice the focal length, the resolving power of your microscope will be doubled. Is his claim valid? Explain.

An astronomer is using a te lescope Lo observe two distant sta rs. The stars are marginally resolved when she looks at them through a filter that passes green light near 550 nm. Which of the following actions would improve the resolution? Assume that the resolution is not limited by the atmosphere. a. Changing the tilter to a different wavelength? If so, should she use a shorter or a longer wavelength? b. Using a telescope with an objective lens of the same diameter but a different focal length? If so, should she select a shorter or a longer focal le ngth? c. Using a telescope with an objective lens of the same focal length but a different diameter? lf so, should she select a larger or a smaller diameter? d. Using an eyepiece with a different magni fi cation? If so, should she select an eyepiece wi th more or less magnification?

A student makes a microscope u ing an objective le ns and an eyepiece. If she moves the lenses closer together, does the microscope's magnification increase or decrease? Explain.

Is the wearer of the glasses in Figure Ql9. 14 nearsighted or farsighted? How can you tell?

A red card is illuminated by red light. What color does it appear to be? What if it's illuminated by blue light?

A collector notices a rare beetle on a tree 1.0 m away. From this vantage point, the beetle has an angular size of 0.69. What would its angular size be if the collector approached it and looked at it with a magnifier having a 5.0 cm focal length? A. 0.69 B. 3.5 C. 6.9 D. 14

A microscope has a Lube length of 20 cm. Whal combination of objective and eyepiece focal lengths will give an overall magnification of I 00? A. 1.5 cm, 3 cm C. I cm, 5 cm B. 2 cm, 2 cm D. 3 cm, 8 cm

The distance between the objective and eyepiece of a telescope is 55 cm. The focal length of the eyepiece is 5.0 cm. What is the angular magnification of this te lescope? A. - 10 B. - 11 C. -50 D. -275

A nearsighted person has a near point of 20 cm and a far point of 40 cm. When he is wearing glasses to correct his distant vision, what is his near point? A. IO cm B. 20 cm C. 40 cm D. 1.0 m

A nearsighted person has a near point of 20 cm and a far point of 40 cm. What refractive power lens is necessary to correct this person's vision to allow her to see distant objects? A. - 5.0 D B. -2.5 D C. +2.5 D D. +5.0 D

A 60-year-old man has a near point of 100 cm, making it impossible to read. What refractive power reading glasses would he need to focus on a newspaper held at a comfortable distance of 40 cm? A. -2.5 D B. - 1.5 D C. + 1.5 D D. +2.5 D

A person looking through a - I 0 D lens sees an image that appears 8.0 cm from the lens. How far from the lens is the object? A. IO cm B. 20cm C.25cm D. 40cm

In a darkened room, red light shines on a red cup, a white card, and a blue toy. The cup, card, and toy will appear, respectively, A. Red, red, blue. B. Red, white, blue. C. Red, red, black. D. Red, black, blue.

An amateur astronomer looks at the moon through a telescope with a 15-cm-diameter objective. What is the minimum separation between two objects on the moon that she can resolve with this telescope? Assume her eye is most sensitive to light with a wavelength of 550 nm. A. 120 m B. 1.7 km C. 26 km D. 520 km

For the combination of two lenses shown in Figure Pl 9.25, find the position, size, and orientation of the final image of the 1.0-cm-tall object.

A researcher is trying to shoot a tranquilizer dart at a 2.0-mtall rhino that is 150 m away. Its angular size as seen through the rifle telescope is 9.1 . What is the magnification of the te lescope?

The objective lens of the refracting telescope at the Lick Observatory in California has a focal length of 57 ft. a. What is the refractive power of this lens? b. What focal length (mm) eyepiece would give a magnification of I OOOX for this telescope?

You use your 8X binoculars to focus on a yellow-rumped warbler (length 14 cm) in a tree 18 m away from you. What angle (in degrees) does the image of the warbler subtend on your retina?

Your telescope has a 700-mmfocal- length objective and a 26-mm-focal -length eyepiece. One evening you decide to look at the full )lloon, which has an angular size of 0.52 when viewed with the naked eye. a. What angle (in degrees) does the image of the moon subtend when you look at it through your telescope? b. Suppose you decide to take a photograph of the moon using your telescope. You posifion a CCD detector so that it captures the image produced by the objective lens. What is the diameter of that image?

A narrow beam of light with wavelengths from 450 nm to 700 nm is incident perpendicular to one face of a 40.00 prism made of crown glass, for which the index of refraction ranges from n = 1.533 to n = 1.517 for those wavelengths. What is the angular spread of the beam after passing through the prism?

A ray of white light strikes the surface of a 4.0-cm-thick slab of flint glass as shown in Figure P 19.3 1. As the ray enters the glass, it is dispersed into its constituent colors. Estimate how far apart the rays of deepest red and deepest violet light are as they exit the bottom surface. Which exiting ray is closer to point P?

A ray of red light, for which n = 1.54, and a ray of violet light, for which n = 1.59, travel through a piece of glass. They meet right at the boundary between the glass and the air, and emerge into the air as one ray with an angle of refraction of 22.5. What is the angle between the two rays in the glass?

Two lightbulbs are 1.0 m apart. From what distance can these lightbulbs be marginally resolved by a small telescope with a 4.0-cm-diameter objective lens? Assume that the lens is limited only by diffraction and A = 600 nm.

A 1.0-cm-diameter microscope objective has a focal length of 2.8 mm. lt is used in visible light with a wavelength of 550 nm. a. What js the objective's resolving power if used in air? b. What is the resolving power of the objective if it is used in an oi l-immersion microscope with 110 ;1 = 1.45?

A mic roscope with an objective of focal length 1.6 mm is used to inspect the tiny features of a computer chip. It is desired to resolve two objects only 400 nm apart. What diameter objective is needed if the microscope is used in air with light of wavelength 550 nm?

Suppose you point a pinhole camera at a 15-m-tall tree that is 75 m away. a. If the detector is 22 cm behind the pinhole, what wi ll be the size of the tree's image on the detector? b. If you would like the image to be larger, should you get closer to the tree or farther from the tree? Explain. c. If you had time, you could make the image larger by rebuilding the camera, changing the length or the pinhole size. What one change would give a larger image?

Jason uses a lens with a focal length of 10.0 cm as a magnifier by holding it right up to his eye. He is observing an object that is 8.0 cm from the lens. What is the a ngular magnification of the lens u ed this way if Jason's near-point distance is 25 cm?

A magnifier is labeled "5X." What would its magnification be if used by a person with a near-point distance of 50 cm?

A 20 X microscope objective is designed for use in a microscope wi th a 16 cm tube length. The objective is marked NA = 0.40. What is the diameter of the objective le ns?

Two converging lenses with focal lengths of 40 cm and 20 cm are 10 cm apart. A 2.0-cm-tall object is 15 cm in fro nt of the 40-cm-focal- length lens. a. Use ray tracing to find the position and height of the image. To do this accurately use a ruler or paper with a grid. Dete rmine the image distance and image height by making measurements on your diagram. b. Calcul ate the image height and image position relative to the second lens. Compare with your ray-tracing answers in pa1t a.

converging lens with a focal length of 40 cm and a diverging lens with a focal length of -40 cm are 160 cm apart. A 2.0-cm-tall object is 60 cm in front of the converging lens. a. Use ray tracing to find the position and height of the image. To do this, accurately use a ruler or paper with a grid. Determine the image distance and image height by maki ng measurements on your diagram. b. Calculate the image height and image position relative to the econd lens. Compare with your ray-tracing answers in part a.

A lens with a focal length of 25 cm is placed 40 cm in front of a lens with a focal length of 5.0 cm. How far from the second lens is the final image of an object infinitely far from the first lens? ls this image in front of or behind the second lens?

A microscope with a 5 X objective lens images a 1.0-mmdiameter specimen. What is the diameter of the real image of this specimen formed by the objective len

Your task in physics lab is to make a microscope from two lenses. One lens has a focal length of I 0 cm, the other a focal length of 3.0 cm. You plan to use the more powerful lens as the objective, and you want its image to be 16 cm from the lens, as in a standard biological microscope. a. How far should the objective lens be from the object to produce a real image 16 cm from the objective? b. What will be the magnification of your microscope?

A 20 X objective and I 0 x eyepiece give an angular magnification of 200 X when used in a microscope with a 160 mm tube length. What magnification would this objective and eyepiece give if used in a microscope with a 200 mm tube length?

The objective lens and the eyepiece lens of a telescope are 1.0 m apart. The telescope has an angular magnification of 50. Find the focal lengths of the eyepiece and the objective.

Your telescope has an objective lens with a focal length of 1.0 m. You point the telescope at the moon, only to realize that the eyepiece is missing. Even so, you can still see the real image of the moon formed by the objective lens if you place your eye a little past the image so as to view the rays diverging from the image plane, j ust as rays would diverge from an object at that location. What is the angular magnification of the moon if you view its real image from 25 cm away, your near-point distance?

Manha is viewing a distant mountain with a telescope that has a 120-cm-focal-length objective lens and an eyepiece with a 2.0 cm focal le ngth. She sees a bird that's 60 m distant and wants to observe it. To do so, she has to refocus the telescope. By how far and in which direction (toward or away from the objective) must she move the eyepiece in order to focus on the bird?

Susan is quite nearsighted; without her glasses, her far point is 35 cm and her near point is 15 cm. Her glasses allow her to view distant objects with her eye relaxed. With her glasses on, what is the closest object on which she can focus?

A spy satellite uses a telescope with a 2.0-m-diameter mirror. It orbits the eaJth at a height of 220 km. What minimum spacing must the re be between two objects on the earth's surface if they are to be resolved as distinct objects by this telescope? Assume the telescope's resolution is limited only by diffraction and that it is recording light with a wavelength of 500 nm.

Two stars have an angular separation of 3.3 X I o-6 rad. What diameter te lescope objective is necessary to just resolve these two stars, using light with a wavelength of 650 nm?

Frank is nearsighted and his glasses require a prescription of - 1.5 D. One day he can't find his glasses, but he does find an older pair with a prescription of - 1.0 D. What is the most distant object that Frank can focus on while wearing this older pair of glasses?

What is the angular resolution of the Hubble Space Telescope's 2.4-m-diameter mirror when viewing light with a wavelength of 550 nm? The resolution of a reflecting telescope is calculated exactly the same as for a refracting telescope.

The Hubble Space Telescope has a mirror diameter of 2.4 m. MCAT-Style Passage Problems Suppose the telescope was used to photograph the surface of the moon from a distance of 3.8 x 108 m. What is the distance Surgical Vision Correction BIO between two objects that the telescope can barely resolve? Assume the wavelength of light is 600 nm.

Once dark adapted, the pupil of your eye is approximately 7 mm in diameter. The headlights of an oncoming car are 120 cm apart. If the lens of your eye is limited only by diffraction, at what distance are the two headlights marginally resolved? Assume the light's wavelength in air is 600 nm and the index of refraction inside the eye is 1.33. (Your eye is not really good eno ugh to resolve headlights at this distance, due both to abe1Tations in the lens and to the size of the receptors in your reti na, but it comes reasonably close.)

The normal human eye has maximum visual acuity with a pupil size of about 3 mm. For larger pupils, acuity decreases due to increasing aberrations; for smaller pupil s, acuity decreases due to increasing effects of diffraction. If your pupil diameter is 2.0 mm, as it would be in fairly bright light, what is the smallest diameter circle that you can barely see as a circle, rather than j ust a dot, if the c ircle is at your near point, 25 cm from your eye? Assume the light's wavelength in air is 600 nm and the index of refraction inside the eye is 1.33.

Microtubules are filamentous structures in cells that maintain cell shape and facilitate the movement of molecules within the cell. They are long, hollow cylinders with a diameter of about 25 nm. It is possible to incorporate fluorescent molecules into microtubules; when illuminated by an ultraviolet light, the fluorescent molecules emit visible light that can be imaged by the optical system of a microscope. Jf the emitted light has a wavelength of 500 nm and the NA of the microscope objective is 1.4, can a biologist looking through the microscope tell whether she is looking at a single microtubule or at two microtubules lying side by side?

Flattening the cornea would be a good solution for someone who was A. Nearsighted. B. Farsighted. C. Either nearsighted or farsighted.

Suppose a woman has a far point of 50 cm. How much should the refractive power of her cornea be changed to correct her vision? A. - 2.0 D B. - 1.0 D C. + 1.0 D D. +2.0 D

A cataract is a clouding or opaci ty that develops in the eye's lens, often in older people. In extreme cases, the lens of the eye may need to be removed. This would have the effect of leaving a person A. Nearsighted. B. Farsighted.

The length of your eye decreases slightly as you age, making the lens a bit closer to the retina. Suppose a man had his vision surgically c01Tected at age 30. At age 70, once his eyes had decreased slightly in length, he would be A. Nearsighted. :S. Farsighted. C. Neither nearsighted nor farsighted.