What is color constancy, and what are its limitations?

Problem 1CQ If the lens of a person’s eye is removed because of cataracts (as has been done since ancient times), why would you expect a spectacle lens of about 16 D to be prescribed?

Problem 1PE Unless otherwise stated, the lens-to-retina distance is 2.00 cm. What is the power of the eye when viewing an object 50.0 cm away?

Problem 2PE Unless otherwise stated, the lens-to-retina distance is 2.00 cm. Calculate the power of the eye when viewing an object 3.00 m away.

Problem 39PE Integrated Concepts (a) During laser vision correction, a brief burst of 193 nm ultraviolet light is projected onto the cornea of the patient. It makes a spot 1.00 mm in diameter and deposits 0.500 mJ of energy. Calculate the depth of the layer ablated, assuming the corneal tissue has the same properties as water and is initially at 34.0ºC . The tissue’s temperature is increased to 100ºC and evaporated without further temperature increase. (b) Does your answer imply that the shape of the cornea can be finely controlled?

Problem 3CQ When laser light is shone into a relaxed normal-vision eye to repair a tear by spot-welding the retina to the back of the eye, the rays entering the eye must be parallel. Why?

Problem 2CQ A cataract is cloudiness in the lens of the eye. Is light dispersed or diffused by it?

Problem 3PE Unless otherwise stated, the lens-to-retina distance is 2.00 cm. (a) The print in many books averages 3.50 mm in height. How high is the image of the print on the retina when the book is held 30.0 cm from the eye? (b) Compare the size of the print to the sizes of rods and cones in the fovea and discuss the possible details observable in the letters. (The eye-brain system can perform better because of interconnections and higher order image processing.)

Problem 4CQ How does the power of a dry contact lens compare with its power when resting on the tear layer of the eye? Explain.

Problem 4PE Unless otherwise stated, the lens-to-retina distance is 2.00 cm. Suppose a certain person’s visual acuity is such that he can see objects clearly that form an image 4.00 ?m high on his retina. What is the maximum distance at which he can read the 75.0 cm high letters on the side of an airplane?

Problem 6CQ It has become common to replace the cataract-clouded lens of the eye with an internal lens. This intraocular lens can be chosen so that the person has perfect distant vision. Will the person be able to read without glasses? If the person was nearsighted, is the power of the intraocular lens greater or less than the removed lens?

Problem 5CQ Why is your vision so blurry when you open your eyes while swimming under water? How does a face mask enable clear vision?

Problem 5PE Unless otherwise stated, the lens-to-retina distance is 2.00 cm. People who do very detailed work close up, such as jewellers, often can see objects clearly at much closer distance than the normal 25 cm. (a) What is the power of the eyes of a woman who can see an object clearly at a distance of only 8.00 cm? (b) What is the size of an image of a 1.00 mm object, such as lettering inside a ring, held at this distance? (c) What would the size of the image be if the object were held at the normal 25.0 cm distance?

Problem 6PE What is the far point of a person whose eyes have a relaxed power of 50.5 D?

Problem 7CQ If the cornea is to be reshaped (this can be done surgically or with contact lenses) to correct myopia, should its curvature be made greater or smaller? Explain. Also explain how hyperopia can be corrected.

Problem 7PE What is the near point of a person whose eyes have an accommodated power of 53.5 D?

Problem 8CQ If there is a fixed percent uncertainty in LASIK reshaping of the cornea, why would you expect those people with the greatest correction to have a poorer chance of normal distant vision after the procedure?

Problem 9PE In a LASIK vision correction, the power of a patient’s eye is increased by 3.00 D. Assuming this produces normal close vision, what was the patient’s near point before the procedure?

Problem 10CQ A pure red object on a black background seems to disappear when illuminated with pure green light. Explain why.

Problem 11CQ What is color constancy, and what are its limitations?

Problem 9CQ A person with presbyopia has lost some or all of the ability to accommodate the power of the eye. If such a person’s distant vision is corrected with LASIK, will she still need reading glasses? Explain.

Problem 10PE What was the previous far point of a patient who had laser vision correction that reduced the power of her eye by 7.00 D, producing normal distant vision for her?

Problem 11PE A severely myopic patient has a far point of 5.00 cm. By how many diopters should the power of his eye be reduced in laser vision correction to obtain normal distant vision for him?

Problem 12CQ There are different types of color blindness related to the malfunction of different types of cones. Why would it be particularly useful to study those rare individuals who are color blind only in one eye or who have a different type of color blindness in each eye?

Problem 12PE A student’s eyes, while reading the blackboard, have a power of 51.0 D. How far is the board from his eyes?

Problem 13PE The power of a physician’s eyes is 53.0 D while examining a patient. How far from her eyes is the feature being examined?

Problem 14CQ Geometric optics describes the interaction of light with macroscopic objects. Why, then, is it correct to use geometric optics to analyse a microscope’s image?

Problem 14PE A young woman with normal distant vision has a 10.0% ability to accommodate (that is, increase) the power of her eyes. What is the closest object she can see clearly?

Problem 15CQ The image produced by the microscope in Figure 26.16 cannot be projected. Could extra lenses or mirrors project it? Explain.

Problem 15PE The far point of a myopic administrator is 50.0 cm. (a) What is the relaxed power of his eyes? (b) If he has the normal 8.00% ability to accommodate, what is the closest object he can see clearly?

Problem 16PE A very myopic man has a far point of 20.0 cm. What power contact lens (when on the eye) will correct his distant vision?

Problem 16CQ Why not have the objective of a microscope form a case 2 image with a large magnification? (Hint: Consider the location of that image and the difficulty that would pose for using the eyepiece as a magnifier.)

Problem 17CQ What advantages do oil immersion objectives offer?

Problem 17PE Repeat the previous problem for eyeglasses held 1.50 cm from the eyes. Reference Previous Problem: A very myopic man has a far point of 20.0 cm. What power contact lens (when on the eye) will correct his distant vision?

Problem 18PE A myopic person sees that her contact lens prescription is –4.00 D . What is her far point?

Problem 18CQ How does the NA of a microscope compare with the NA of an optical fiber?

Problem 19CQ If you want your microscope or telescope to project a real image onto a screen, how would you change the placement of the eyepiece relative to the objective?

Problem 19PE Repeat the previous problem for glasses that are 1.75 cm from the eyes. Reference Previous Problem: A myopic person sees that her contact lens prescription is –4.00 D . What is her far point?

Problem 20PE The contact lens prescription for a mildly farsighted person is 0.750 D, and the person has a near point of 29.0 cm. What is the power of the tear layer between the cornea and the lens if the correction is ideal, taking the tear layer into account?

Problem 22PE A mother sees that her child’s contact lens prescription is 0.750 D. What is the child’s near point?

Problem 21PE A nearsighted man cannot see objects clearly beyond 20 cm from his eyes. How close must he stand to a mirror in order to see what he is doing when he shaves?

Problem 23PE Repeat the previous problem for glasses that are 2.20 cm from the eyes. Reference Previous Problem: A mother sees that her child’s contact lens prescription is 0.750 D. What is the child’s near point?

Problem 24PE The contact lens prescription for a nearsighted person is –4.00 D and the person has a far point of 22.5 cm. What is the power of the tear layer between the cornea and the lens if the correction is ideal, taking the tear layer into account?

Problem 25PE Unreasonable Results A boy has a near point of 50 cm and a far point of 500 cm. Will a –4.00 D lens correct his far point to infinity?

Problem 26PE A microscope with an overall magnification of 800 has an objective that magnifies by 200. (a) What is the magnification of the eyepiece? (b) If there are two other objectives that can be used, having magnifications of 100 and 400, what other total magnifications are possible?

Problem 27PE (a) What magnification is produced by a 0.150 cm focal length microscope objective that is 0.155 cm from the object being viewed? (b) What is the overall magnification if an 8× eyepiece (one that produces a magnification of 8.00) is used?

Problem 28PE (a) Where does an object need to be placed relative to a microscope for its 0.500 cm focal length objective to produce a magnification of –400 ? (b) Where should the 5.00 cm focal length eyepiece be placed to produce a further fourfold (4.00) magnification?

Problem 29PE You switch from a 1.40NA 60× oil immersion objective to a 1.40NA 60× oil immersion objective. What are the acceptance angles for each? Compare and comment on the values. Which would you use first to locate the target area on your specimen?

An amoeba is \(0.305 \ cm\) away from the \(0.300 \ cm\) focal length objective lens of a microscope. (a) Where is the image formed by the objective lens? (b) What is this image’s magnification? (c) An eyepiece with a \(2.00 \ cm\) focal length is placed \(20.0 \ cm\) from the objective. Where is the final image? (d) What magnification is produced by the eyepiece? (e) What is the overall magnification? (See Figure 26.16.) Equation Transcription: Text Transcription: 0.305 cm 0.300 cm 2.00 cm 20.0 cm

Problem 32PE Unreasonable Results Your friends show you an image through a microscope. They tell you that the microscope has an objective with a 0.500 cm focal length and an eyepiece with a 5.00 cm focal length. The resulting overall magnification is 250,000. Are these viable values for a microscope?

Problem 33PE Unless otherwise stated, the lens-to-retina distance is 2.00 cm. What is the angular magnification of a telescope that has a 100 cm focal length objective and a 2.50 cm focal length eyepiece?

You are using a standard microscope with a \(0.10NA\ 4\times\) objective and switch to a \(0.65\mathrm{NA}\ 40\times\) objective. What are the acceptance angles for each? Compare and comment on the values. Which would you use first to locate the target area on of your specimen? (See Figure 26.17.) Equation Transcription: Text Transcription: 0.10NA 4x 0.65NA 40x

Problem 34PE Unless otherwise stated, the lens-to-retina distance is 2.00 cm. Find the distance between the objective and eyepiece lenses in the telescope in the above problem needed to produce a final image very far from the observer, where vision is most relaxed. Note that a telescope is normally used to view very distant objects.

Problem 35PE Unless otherwise stated, the lens-to-retina distance is 2.00 cm. A large reflecting telescope has an objective mirror with a 10.0 m radius of curvature. What angular magnification does it produce when a 3.00 m focal length eyepiece is used?

Problem 36PE Unless otherwise stated, the lens-to-retina distance is 2.00 cm. A small telescope has a concave mirror with a 2.00 m radius of curvature for its objective. Its eyepiece is a 4.00 cm focal length lens. (a) What is the telescope’s angular magnification? (b) What angle is subtended by a 25,000 km diameter sunspot? (c) What is the angle of its telescopic image?

Problem 37PE Unless otherwise stated, the lens-to-retina distance is 2.00 cm. A 7.5× binocular produces an angular magnification of ?7.50 , acting like a telescope. (Mirrors are used to make the image upright.) If the binoculars have objective lenses with a 75.0 cm focal length, what is the focal length of the eyepiece lenses?

Construct Your Own Problem Consider a telescope of the type used by Galileo, having a convex objective and a concave eyepiece as illustrated in Figure 26.23(a). Construct a problem in which you calculate the location and size of the image produced. Among the things to be considered are the focal lengths of the lenses and their relative placements as well as the size and location of the object. Verify that the angular magnification is greater than one. That is, the angle subtended at the eye by the image is greater than the angle subtended by the object.

Problem 8PE (a) A laser vision correction reshaping the cornea of a myopic patient reduces the power of his eye by 9.00 D, with a ±5.0% uncertainty in the final correction. What is the range of diopters for spectacle lenses that this person might need after LASIK procedure? (b) Was the person nearsighted or farsighted before the procedure? How do you know?

Problem 13CQ Propose a way to study the function of the rods alone, given they can sense light about 1000 times dimmer than the cones.

Problem 20CQ List the various types of aberrations. What causes them and how can each be reduced?