College Physics: A Strategic Approach

Randall D. Knight, Brian Jones, Stuart Field

Chapter 19

Optical Instruments - all with Video Answers

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Chapter Questions

Problem 1

Suppose you point a pinhole camera at a $15-\mathrm{m}$ -tall tree that is $75 \mathrm{m}$ away. If the detector is $22 \mathrm{cm}$ behind the pinhole, what will be the size of the tree's image on the detector?

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 2

A student has built a 20 -cm-long pinhole camera for a science fair project. She wants to photograph the Washington Monument, which is $167 \mathrm{m}(550 \mathrm{ft})$ tall, and to have the image on the detector be $5.0 \mathrm{cm}$ high. How far should she stand from the Washington Monument?

Nathan Silvano

Numerade Educator

Problem 3

A pinhole camera is made from an $80-\mathrm{cm}-$ long box with a small hole in one end. If the hole is $5.0 \mathrm{m}$ from a $1.8-\mathrm{m}$ -tall person, how tall will the image of the person on the detector be? You are taking a picture of a giraffe that is standing far away from you. The image is just too small, so you swap the $50-\mathrm{mm}-$ focal-length lens in your camera for a $600 \mathrm{mm}$ telephoto lens. By what factor does this increase the size of the image?

Nathan Silvano

Numerade Educator

Problem 4

You are taking a picture of a giraffe that is standing far away from you. The image is just too small, so you swap the $50-\mathrm{mm}-$ focal-length lens in your camera for a $600 \mathrm{mm}$ telephoto lens. By what factor does this increase the size of the image?

Nathan Silvano

Numerade Educator

Problem 5

A photographer uses his camera, whose lens has a $50 \mathrm{mm}$ focal length, to focus on an object $2.0 \mathrm{m}$ away. He then wants to take a picture of an object that is $40 \mathrm{cm}$ away. How far, and in which direction, must the lens move to focus on this second object?

Nathan Silvano

Numerade Educator

Problem 6

Turning the barrel of a 50 -mm-focal-length lens on a manualfocus camera moves the lens closer to or farther from the sensor to focus on objects at different distances. The lens has a stated range of focus from $0.45 \mathrm{m}$ to infinity. How far does the lens move between these two extremes?

Nathan Silvano

Numerade Educator

Problem 7

An older camera has a lens with a focal length of $50 \mathrm{mm}$ and uses $36-\mathrm{mm}$ -wide film. Using this camera, a photographer takes a picture of the Golden Gate Bridge that completely spans the width of the film. Now he wants to take a picture of the bridge using his digital camera with its 12-mm-wide CCD detector. What focal length should this camera's lens have for the image of the bridge to cover the entire detector?

Nathan Silvano

Numerade Educator

Problem 8

In old Polaroid cameras, the image was projected on film that developed inside the camera. The developed image was then ejected from the camera as a printed photograph. The standard film size for one popular camera was 79 mm square. The film was $116 \mathrm{mm}$ behind the lens. If you wanted a picture of your $1.6-\mathrm{m}$ -tall friend to fill half the frame, how far away from you did she need to stand?

Narayan Hari

Numerade Educator

Problem 9

In Figure $\mathrm{P} 19.9$ the camera lens has a $50 \mathrm{mm}$ focal length. How high is the man's well-focused image on the CCD detector?

Nathan Silvano

Numerade Educator

Problem 10

A lens with $f=+15 \mathrm{cm}$ is paired with a lens with $f=-20 \mathrm{cm} .$ What is the focal length of the combination?

Nathan Silvano

Numerade Educator

Problem 11

Two converging lenses with focal lengths of $20 \mathrm{cm}$ and $24 \mathrm{cm}$ are combined to make a single lens. What is the focal length of the combination?

Nathan Silvano

Numerade Educator

Problem 12

Oscar has an old-fashioned lantern projector that uses a candle and a lens to project a slide onto the wall. The lens is $1.3 \mathrm{cm}$ from the slide and projects an image onto a screen $80 \mathrm{cm}$ away. Oscar adds a lens to the original lens to allow him to project an image onto a screen $30 \mathrm{cm}$ away.
a. What is the power of the original lens?
b. What is the desired power of the combined lenses?
c. What power lens must Oscar add?

Narayan Hari

Numerade Educator

Problem 13

A+2.0 D lens is being used to make an image of a distant object on a screen. The image is $2.4 \mathrm{cm}$ tall. A second $+2.0 \mathrm{D}$ lens is added to the first, and the lens combination is moved to refocus the image. How tall is the new image?

Narayan Hari

Numerade Educator

Problem 14

If the retina is $1.7 \mathrm{cm}$ from the lens in the eye, how large is the image on the retina of a person of height $1.5 \mathrm{m}$ standing $8.0 \mathrm{m}$ away?

Rashmi Sinha

Numerade Educator

Problem 15

Measure your near point by bringing this page up to the closest distance at which the image is still crisp $-$ not the closest at which you can still read the letters, but the closest at which they remain sharp. (If you wear glasses or contacts, keep them on.) Measure the distance to determine your near point. What is your range of accommodation?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 16

At a distance of 6 meters, a person with average vision is able to clearly read letters $1.0 \mathrm{cm}$ high. Approximately how large do the letters appear on the retina? (Assume that the retina is $1.7 \mathrm{cm}$ from the lens.)

Narayan Hari

Numerade Educator

Problem 17

A farsighted person has a near point of $50 \mathrm{cm}$. What strength lens, in diopters, is needed to bring his near point to $25 \mathrm{cm} ?$

Nathan Silvano

Numerade Educator

Problem 18

Rachel has good distant vision but has a touch of presbyopia. Her near point is $0.60 \mathrm{m}$. When she wears $+2.0 \mathrm{D}$ reading glasses, what is her near point? Her far point?

Narayan Hari

Numerade Educator

Problem 19

A nearsighted woman has a far point of $300 \mathrm{cm}$. What kind of lens, converging or diverging, should be prescribed for her to see distant objects more clearly? What refractive power should the lens have?

Nathan Silvano

Numerade Educator

Problem 20

A nearsighted person has a near point of $12 \mathrm{cm}$ and a far point of $40 \mathrm{cm} .$ What power corrective lens is needed for her to have clear distant vision? With this corrective lens in place, what is her new near point?

Narayan Hari

Numerade Educator

Problem 21

Martin has severe myopia, with a far point of only $17 \mathrm{cm} .$ He wants to get glasses that he'll wear while using his computer, whose screen is $65 \mathrm{cm}$ away. What refractive power is needed for Martin to view the screen with his eyes relaxed?

Narayan Hari

Numerade Educator

Problem 22

Mary's glasses have $+4.0 \mathrm{D}$ converging lenses. This gives her a near point of $20 \mathrm{cm} .$ What is the location of her near point when she is not wearing her glasses?

Narayan Hari

Numerade Educator

Problem 23

Rank the following people from the most nearsighted to the most farsighted, indicating any ties:
A. Bernie has a prescription of $+2.0 \mathrm{D}$
B. Carol needs diverging lenses with a focal length of $-0.35 \mathrm{m}$
C. Maria Elena wears converging lenses with a focal length of $0.50 \mathrm{m}$
D. Janet has a prescription of +2.5 D.
E. Warren's prescription is $-3.2 \mathrm{D}$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 24

With -5.0 D corrective lenses, Juliana's distant vision is quite sharp. She has a pair of -3.5 D computer glasses that puts her computer screen right at her far point. How far away is her computer?

Prashant Bana

Numerade Educator

Problem 25

The rod and cone cells in the central part of the retina - the fovea - are packed closer together, giving a more detailed view. This area of increased rod and cone density has a diameter of about $1.5 \mathrm{mm} .$ When you read a book, you want the image of the text you are reading to fall on the fovea. If you hold a book $30 \mathrm{cm}$ from your eyes, how wide is the spot on the page whose image just fills the fovea? (Assume that the retina is $1.7 \mathrm{cm}$ from the lens.)

Anand Jangid

Numerade Educator

Problem 26

A jeweler is wearing a $20 \mathrm{D}$ magnifying lens directly in front of his eye. If his near point is a typical $25 \mathrm{cm},$ how close can he hold a gem that he is inspecting?

Narayan Hari

Numerade Educator

Problem 27

Oliver has had a stamp collection since he was a boy. In those days, holding a stamp $10 \mathrm{cm}$ from his eye gave him a clear image. Now, his near point has receded to $90 \mathrm{cm},$ so he holds a magnifying lens directly in front of his eye to let him bring stamps closer. To the nearest diopter, what power lens enables him to focus on a stamp $10 \mathrm{cm}$ away?

Narayan Hari

Numerade Educator

Problem 28

Anna holds a 12 D magnifier directly in front of her eye to get a close look at a 19 -mm-diameter penny. What is the closest possible distance that she can hold the coin to have it appear in focus? At this distance, how large does the image of the coin appear on her retina? (Assume a typical $25 \mathrm{cm}$ near point and a distance of $1.7 \mathrm{cm}$ between the lens and the retina.)

Narayan Hari

Numerade Educator

Problem 29

The diameter of a penny is $19 \mathrm{mm}$. As we've seen, the moon subtends an angle of approximately $0.5^{\circ}$ in the sky. How far from your eye must a penny be held so that it has the same apparent size as the moon?

Narayan Hari

Numerade Educator

Problem 30

When you solder electronic components, you want to keep your face away from the work but still be able to see it clearly, so you use a soldering station with a built-in lens. Clips hold the work you are soldering, and a flexible arm holds the lens above the work. You view the work from some distance, but the area under the lens is magnified enough that you can see fine details. A typical magnifier is rated at $3 \times .$ How far from the work should the lens be placed?

Narayan Hari

Numerade Educator

Problem 31

A magnifier has a magnification of $5 \times .$ How far from the lens should an object be placed so that its (virtual) image is at the near-point distance of $25 \mathrm{cm} ?$

Narayan Hari

Numerade Educator

Problem 32

People with compromised vision can buy full-page magnifiers that enlarge printed materials to a size that they can more easily read. A typical magnifier is rated at $2 \times$ magnification and is held in a stand above the page. How far from the page is the magnifier?

Narayan Hari

Numerade Educator

Problem 33

A student microscope has an objective lens that is labeled with a magnification of $10 \times .$ Assume a length $L=120 \mathrm{mm}$
a. What is the focal length of the objective lens?
b. What focal length eyepiece lens is needed to give an overall magnification of $150 \times ?$

Narayan Hari

Numerade Educator

Problem 34

You are using a microscope with a $10 \times$ eyepiece. What focal length of the objective lens will give a total magnification of $200 \times ?$ Assume a length $L=160 \mathrm{mm}$.

Narayan Hari

Numerade Educator

Problem 35

A forensic scientist is using a microscope with a $15 \times$ objective and a $5 \times$ eyepiece to examine a hair from a crime scene. How far from the objective is the hair? Assume a length $L=160 \mathrm{mm}$

Narayan Hari

Numerade Educator

Problem 36

A microscope has an 8.0 -mm-focal-length objective. For the microscope to be in focus, how far should the objective lens be from the specimen? Assume a length $L=160 \mathrm{mm}$.

Narayan Hari

Numerade Educator

Problem 37

The objective lens of a microscope has a focal length of $5.0 \mathrm{mm} .$ What eyepiece focal length will give the microscope an overall angular magnification of $350 ?$ Assume a length $L=160 \mathrm{mm}$.

Narayan Hari

Numerade Educator

Problem 38

A student microscope has a $10 \times$ objective and a $15 \times$ eyepiece. A student is using the microscope to view a thin slice of an apple. The cells in the apple have a diameter of $0.10 \mathrm{mm}$. Assume a length $L=160 \mathrm{mm}$.
a. How far from the objective lens should the apple slice be placed?
b. How does the angular size of a cell when viewed through the microscope compare to the angular size of a $19-\mathrm{mm}$ -diameter penny at a distance of $25 \mathrm{cm} ?$

Rashmi Sinha

Numerade Educator

Problem 39

For the combination of two identical lenses shown in Figure $\mathrm{P} 19.39,$ find the position, size, and orientation of the final image of the $2.0-\mathrm{cm}-$ tall object.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 40

For the combination of two lenses shown in Figure $\mathrm{P} 19.40,$ find the position, size, and orientation of the final image of the $1.0-\mathrm{cm}-$ tall object.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 41

A researcher is trying to shoot a tranquilizer dart at a 2.0-m-tall rhino that is $150 \mathrm{m}$ away. Its angular size as seen through the rifle telescope is $9.1^{\circ} .$ What is the magnification of the telescope?

Narayan Hari

Numerade Educator

Problem 42

The objective lens of the refracting telescope at the Lick Observatory in California has a focal length of $57 \mathrm{ft} .$
a. What is the refractive power of this lens?
b. What focal length (mm) eyepiece would give a magnification of $1000 \times$ for this telescope?

Narayan Hari

Numerade Educator

Problem 43

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

Narayan Hari

Numerade Educator

Problem 44

Use the astronomical data provided in this text to compute the angular size of Jupiter as seen from earth when the distance from earth to Jupiter is the same as the distance from the sun to Jupiter. Your telescope's objective lens has a focal length of $700 \mathrm{mm},$ and you use a $10 \mathrm{mm}$ eyepiece to view Jupiter. What is the angular size of the image?

Mayukh Banik

Numerade Educator

Problem 45

Your telescope has a 1000 -mm-focal-length objective. You use your telescope to take a photo of the full moon, which has an angular size of $0.52^{\circ}$ that night. You position a $\mathrm{CCD}$ detector so that it captures the image produced by the objective lens. What is the diameter of that image?

Anand Jangid

Numerade Educator

Problem 46

A narrow beam of light with wavelengths from 450 nm to $700 \mathrm{nm}$ is incident perpendicular to one face of a prism made of crown glass, for which the index of refraction ranges from $n=1.533$ to $n=1.517$ for those wavelengths. The light strikes the opposite side of the prism at an angle of $40^{\circ} .$ What is the angular spread of the beam as it leaves the prism?

Penny Riley

Numerade Educator

Problem 47

A ray of white light strikes the surface of a $4.0-\mathrm{cm}$ -thick slab of flint glass as shown in Figure $P 19.47$. 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?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 48

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 $22.5^{\circ} .$ What is the angle between the two rays in the glass?

Narayan Hari

Numerade Educator

Problem 49

The near point for your myopic uncle is $10 \mathrm{cm} .$ Your own vision is normal; that is, your near point is $25 \mathrm{cm} .$ Suppose you and your uncle hold dimes (which are $1.7 \mathrm{cm}$ in diameter) at your respective near points.
a. For you, what is the dime's angular size, in radians?
b. For your uncle, what is the dime's angular size, in radians?
c. Do these calculations suggest any benefit to nearsightedness?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 50

Two lightbulbs are $1.0 \mathrm{m}$ 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 $\lambda=600 \mathrm{nm}$.

Narayan Hari

Numerade Educator

Problem 51

A $1.0-\mathrm{cm}$ -diameter microscope objective has a focal length of $2.8 \mathrm{mm} .$ It is used with light of wavelength of $550 \mathrm{nm}$.
a. What is the objective's resolving power if used in air?
b. What is the resolving power of the objective if it is used in an oil-immersion microscope with $n_{\text {eal }}=1.45 ?$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 52

Makers of cameras often use pixel count as an indicator of quality, and add sensors with more and more pixels. But the number of pixels is only one determinant of image quality. If the width of the central maximum of a diffraction pattern is larger than twice the spacing between the pixels, then packing the pixels more densely won't change the image quality. It's hard to get a camera with good optical quality in a smartphone; the lens must be small, so diffraction will be an issue. One smartphone manufacturer includes a camera with $20.7 \mathrm{MP}$ which sounds very good. But let's look at the numbers: The distance between the pixels is $1.2 \mu \mathrm{m} ;$ the focal length of the lens is $4.8 \mathrm{mm},$ with a $2.2-\mathrm{mm}$ -diameter aperture. For $600 \mathrm{nm}$ light, what is the width of the central maximum? Could a sensor with more widely spaced pixels provide similar image quality?

Ajay Singhal

Numerade Educator

Problem 53

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

Narayan Hari

Numerade Educator

Problem 54

Suppose you are on a planet orbiting a star 10 light years away. (One light year is the distance light travels in one year.) At this distance, what is the minimum diameter for an objective mirror that will just barely resolve the earth and the sun? Assume a wavelength of $600 \mathrm{nm}$. (Astronomers have discovered many worlds around nearby stars, but this has been done by indirect means. It's a tall order to obtain a picture of a planet around a star. The problem isn't resolution; it's the great difference in brightness between the two objects.)

Narayan Hari

Numerade Educator

Problem 55

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

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 56

A magnifier is labeled "5 $\times$ " What wonld its magnification be if used by a person with a near-point distance of $50 \mathrm{cm} ?$

Narayan Hari

Numerade Educator

Problem 57

What is the diameter of the objective lens? Assume a length $L=160 \mathrm{mm}$

Narayan Hari

Numerade Educator

Problem 58

Two converging lenses with focal lengths of $40 \mathrm{cm}$ and $20 \mathrm{cm}$ are $10 \mathrm{cm}$ apart. A $2.0-\mathrm{cm}$ -tall object is $15 \mathrm{cm}$ in front of the $40-\mathrm{cm}-$ 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. Determine the image distance and image height by making measurements on your diagram.
b. Calculate the image height and position relative to the second lens. Compare with your ray-tracing answers in part a.

Ajay Singhal

Numerade Educator

Problem 59

A converging lens with a focal length of $40 \mathrm{cm}$ and a diverging lens with a focal length of $-40 \mathrm{cm}$ are $160 \mathrm{cm}$ apart.
A 2.0 -cm-tall object is $60 \mathrm{cm}$ 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 making measurements on your diagram.
b. Calculate the image height and image position relative to the second lens. Compare with your answers in part a.

Sean Dougherty

Numerade Educator

Problem 60

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

Narayan Hari

Numerade Educator

Problem 61

A microscope with a $5 \times$ objective lens images a 1.0 -mmdiameter specimen. What is the diameter of the real image of this specimen formed by the objective lens?

Narayan Hari

Numerade Educator

Problem 62

Your task in physics lab is to make a microscope from two lenses. One lens has a focal length of $10 \mathrm{cm},$ the other a focal length of $3.0 \mathrm{cm} .$ You plan to use the more powerful lens as the objective, and you want its image to be $16 \mathrm{cm}$ 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 $16 \mathrm{cm}$ from the objective?
b. What will be the magnification of your microscope?

Narayan Hari

Numerade Educator

Problem 63

The objective lens and the eycpiece lens of a telescope are $1.0 \mathrm{m}$ apart. The telescope has an angular magnification of $50 .$ Find the focal lengths of the eyepiece and the objective.

Narayan Hari

Numerade Educator

Problem 64

Your telescope has an objective lens with a focal length of $1.0 \mathrm{m} .$ You point the telescope at the moon, then realize that the eyepiece is missing. 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, just 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 $25 \mathrm{cm}$ away, your near-point distance?

Narayan Hari

Numerade Educator

Problem 65

Martha is viewing a distant mountain with a telescope that has a $120-\mathrm{cm}$ -focal-length objective lens and an eyepiece with a $2.0 \mathrm{cm}$ focal length. She sees a bird that's $60 \mathrm{m}$ 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?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 66

Susan is quite nearsighted; without her glasses, her far point is $35 \mathrm{cm}$ and her near point is $15 \mathrm{cm} .$ 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?

Narayan Hari

Numerade Educator

Problem 67

A spy satellite uses a telescope with a 2.0 - m-diameter mirror. It orbits the earth at a height of $220 \mathrm{km}$. What minimum spacing must there 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 records 500 nm light.

Narayan Hari

Numerade Educator

Problem 68

If Two stars have an angular separation of $3.3 \times 10^{-6}$ rad. What diameter telescope objective is necessary to just resolve these two stars, using light with a wavelength of $650 \mathrm{nm} ?$

Narayan Hari

Numerade Educator

Problem 69

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 $-1.0 \mathrm{D}$. What is the most distant object that Frank can focus on while wearing this older pair of glasses?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 70

All eyeglass lenses have chromatic aberration. This is usually expressed as dioptric spread. For a typical $+6.0 \mathrm{D}$ lens, the focusing power for red light is $+5.90,$ the power for green light is $+6.00 \mathrm{D},$ and the power for blue light is $+6.10 .$ This gives a dioptric spread of 0.20 diopter. Suppose a myopic person is observing a distant object through this lens, and the green light of the image is in perfect focus. Assume a distance $s^{\prime}=1.7000 \mathrm{cm} .$ How far in front of or behind the retina is the point of sharp focus for red light? For blue light? (In practice, this amount of dioptric spread is fine; eyeglass wearers don't notice anything less than a spread of 0.30 diopter.)

Narayan Hari

Numerade Educator

Problem 71

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

Narayan Hari

Numerade Educator

Problem 72

The Hubble Space Telescope has a mirror diameter of $2.4 \mathrm{m}$. Suppose the telescope was used to photograph the surface of the moon from a distance of $3.8 \times 10^{8} \mathrm{m} .$ What is the distance between two objects that the telescope can barely resolve? Assume the wavelength of light is $600 \mathrm{nm}$.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 73

Once dark adapted, the pupil of your eye is approximately $7 \mathrm{mm}$ in diameter. The headlights of an oncoming car are $120 \mathrm{cm}$ apart. If the resolution 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 $600 \mathrm{nm}$ and the index of refraction inside the eye is $1.33 .$ (Your eye is not really good enough to resolve headlights at this distance, due to aberrations in the lens.)

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 74

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

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 75

Microtubules are 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 $25 \mathrm{nm}$. It is possible to incorporate fluorescent molecules into microtubules; when illuminated by ultraviolet light, the fluorescent molecules emit visible light that can be imaged by the optical system of a microscope. If the emitted light has a wavelength of $500 \mathrm{nm}$ 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?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 76

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

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 77

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

Narayan Hari

Numerade Educator

Problem 78

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 corrected at age $30 .$ At age $70,$ once his eyes had decreased slightly in length, he would be
A. Nearsighted.
B. Farsighted.
C. Neither nearsighted nor farsighted.

Narayan Hari

Numerade Educator