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Physics

James S. Walker

Chapter 27

Optical lnstruments - all with Video Answers

Educators


Chapter Questions

01:45

Problem 1

Predict/Explain Octopus Eyes To focus its eyes, an octopus does not change the shape of its lens, as is the case in humans. Instead, an octopus moves its rigid lens back and forth, as in a camera. This changes the distance from the lens to the retina and
brings an object into focus. (a) If an object moves closer to an octopus, must the octopus move its lens closer to or farther from its
retina to keep the object in focus? (b) Choose the best explanation
from among the following:
I. The lens must move closer to the retina-that is, farther away
from the object-to compensate for the object moving closer
to the eye.
II. When the object moves closer to the eye, the image produced
by the lens will be farther behind the lens; therefore, the lens
must move farther from the retina.

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05:09

Problem 2

Your friend is 1.7 $\mathrm{m}$ tall. (a) When she stands 3.2 $\mathrm{m}$ from you,
what is the height of her image formed on the retina of your eye?
(Consider the eye to consist of a thin lens 2.5 $\mathrm{cm}$ from the retina.)
(b) What is the height of her image when she is 4.2 $\mathrm{m}$ from you?

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04:18

Problem 3

Which forms the larger image on the retina of your eye: a $43-$ ft
tree seen from a distance of 210 ft, or a 12 -in. flower viewed from
a distance of 2.0 $\mathrm{ft}$ ?

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03:03

Problem 4

Approximating the eye as a single thin lens 2.70 $\mathrm{cm}$ from the retina, find the eye's near-point distance if the smallest focal length the eye can produce is 2.10 $\mathrm{cm} .$

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03:06

Problem 5

Approximating the eye as a single thin lens 2.70 $\mathrm{cm}$ from the
retina, find the focal length of the eye when it is focused on an
object at a distance of (a) 255 $\mathrm{cm}$ and (b) 25.5 $\mathrm{cm} ?$

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02:57

Problem 6

Find the far-point distance of a person whose relaxed eye has a
focal length of 2.68 $\mathrm{cm}$ , treating the eye as if it were a single thin
lens 2.71 $\mathrm{cm}$ from the retina.

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03:23

Problem 7

Four camera lenses have the following focal lengths and
$f$ -numbers:
Rank these lenses in order of increasing aperture diameter. Indicate ties where appropriate.

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02:01

Problem 8

The focal length of the human eye is approximately 1.7 $\mathrm{cm} .$
(a) What is the $f$ -number for the human eye in bright light, when
the pupil diameter is 2.0 $\mathrm{mm}$ ? (b) What is the $f$ -number in dim
light, when the pupil diameter has expanded to 7.0 $\mathrm{mm}$ ?

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03:01

Problem 9

Predict/Calculate A camera with a 65 -mm-focal-length lens has
aperture $f$ -numbers of $2.8,4,8,11,$ and $16 .$ (a) Which setting has
the largest aperture diameter? (b) Calculate the five possible aperture diameters for this camera.

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04:54

Problem 10

The actual light sensor size of a digital camera is 14.9 $\mathrm{mm} \times$
22.3 $\mathrm{mm} .$ You want to take a photo of your friend, who is 1.9 $\mathrm{m}$
tall. Your camera has a $55-\mathrm{mm}$ -focal-length lens. How far from the camera should your friend stand in order to produce a $22-\mathrm{mm}$ -tall
image on the light sensor?

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02:21

Problem 11

(a) Find the $f$ -number of a telescope with an objective diameter of
8.3 $\mathrm{cm}$ and a focal length of 91 $\mathrm{cm} .$ (b) Find the aperture diameter of
an $f / 1.2$ all-sky meteor camera lens with a focal length of 2.5 $\mathrm{mm} .$

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04:40

Problem 12

You are taking a photo of a poster on the wall of your dorm
room, so you can't back away any farther than 3.0 $\mathrm{m}$ to take the
shot. The poster is 0.80 $\mathrm{m}$ wide and 1.2 $\mathrm{m}$ tall, and you want the
image to fit on the $15-\mathrm{mm} \times 22$ -mm image sensor in your camera. What is the longest focal length lens that will work?

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06:45

Problem 13

You are taking pictures of the beach at sunset. Just before the Sun
sets, a shutter speed of 1$/ 100$ and an aperture of $f / 11$ produces a
properly exposed picture. Shortly after the Sun sets, however, your
light meter indicates that the scene is only one-quarter as bright
as before. (a) If you don't change the aperture, what approximate
shutter speed is needed for your second shot? (b) If, instead, you
keep the shutter speed at 1$/ 100$ s, what approximate $f$ -stop will be
needed for the second shot?

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05:49

Problem 14

Predict/Calculate You are taking a photograph of a horse
race. A shutter speed of 125 at $f / 5.6$ produces a properly exposed
image, but the running horses give a blurred image. Your camera
has $f$ -stops of $2,2.8,4,5.6,8,11,$ and $16 .$ (a) To use the shortest
possible exposure time (i.e., highest shutter speed), which $f$ -stop
should you use? (b) What is the shortest exposure time you can
use and still get a properly exposed image?

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02:09

Problem 15

The Hale Telescope The 200 -in. $(5.08-m)$ diameter mirror of the
Hale telescope on Mount Palomar has a focal length $f=16.9 \mathrm{m}$ .
(a) When the detector is placed at the focal point of the mirror
(the "prime focus"), what is the $f$ -number for this telescope?
(b) The coude focus arrangement uses additional mirrors to bend
the light path and increase the effective focal length to 155.4 $\mathrm{m}$ .
What is the $f$ -number of the telescope when the coude focus is
being used? (Coude is French for "elbow," since the light path is
"bent like an elbow." This arrangement is useful when the light
needs to be focused onto a distant instrument.)

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01:26

Problem 16

Predict/Explain Two professors are stranded on a deserted
island. Both wear glasses, though one is nearsighted and the other
is farsighted. (a) Which person's glasses should be used to focus
the rays of the Sun and start a fire? (b) Choose the best explanation
from among the following:
I. A nearsighted person can focus close, so that person's glasses
should be used to focus the sunlight on a piece of moss at a
distance of a couple inches.
II. A farsighted person can't focus close, so the glasses to correct
that person's vision are converging. A converging lens is what
you need to concentrate the rays of the Sun.

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02:04

Problem 17

A clerk at the local grocery store wears glasses that make her
eyes look larger than they actually are. Is the clerk nearsighted or
farsighted? Explain.

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01:46

Problem 18

The umpire at a baseball game wears glasses that make his
eyes look smaller than they actually are. Is the umpire nearsighted
or farsighted? Explain.

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02:26

Problem 19

A police detective discovers eyeglasses with a focal length of
$-80.0 \mathrm{cm}$ at a crime scene. (a) If the eyeglasses belong to the suspect, is the suspect nearsighted or farsighted? Explain. (b) A search of a person's home reveals an eyeglass prescription of $-0.80$ diopter. Is the person the suspect? Explain.

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01:26

Problem 20

The cornea of a normal human eye has an optical power of
$+44.0$ diopters. What is its focal length?

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01:40

Problem 21

A myopic student is shaving without his glasses. If his eyes have a
far point of $1.9 \mathrm{m},$ what is the greatest distance he can stand from
the mirror and still see his image clearly?

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01:06

Problem 22

An eyeglass prescription calls for a lens with an optical power of
$+2.9$ diopters. What is the focal length of this lens?

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02:01

Problem 23

An optometrist prescribes contact lenses with a power of $-0.75$
diopter for you. What is your far-point distance?

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01:32

Problem 24

Two thin lenses, with $f_{1}=+25.0 \mathrm{cm}$ and $f_{2}=-42.5 \mathrm{cm},$ are
placed in contact. What is the focal length of this combination?

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07:47

Problem 25

Two concave lenses, each with $f=-15 \mathrm{cm},$ are separated by
7.5 $\mathrm{cm} .$ An object is placed 25 $\mathrm{cm}$ in front of one of the lenses. Find
(a) the location and (b) the magnification of the final image produced by this lens combination.

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03:21

Problem 26

Predict/Calculate The focal length of a relaxed human
eye is approximately 1.7 $\mathrm{cm} .$ When we focus our eyes on a close-up object, we can change the refractive power of the eye by about 16 diopters. (a) Does the refractive power of our eyes increase or
decrease by 16 diopters when we focus closely? Explain. (b) Calculate the focal length of the eye when we focus closely.

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03:18

Problem 27

Predict/Calculate Diopter Change in Diving Cormorants Double-crested cormorants (Phalacrocorax auritus) are extraordinary
birds-they can focus on objects in the air, just like we can, but
they can also focus underwater as they pursue their prey. To do so, they have one of the largest accommodation ranges in nature-that is,
they can change the focal length of their eyes by amounts that are
greater than is possible in other animals. When a cormorant plunges
into the ocean to catch a fish, it can change the refractive power of its eyes by about 45 diopters, as compared to only 16 diopters of change
possible in the human eye. (a) Should this change of 45 diopters be
an increase or a decrease? Explain. (b) If the focal length of the cormorant's eyes is 4.2 $\mathrm{mm}$ before it enters the water, what is the focal
length after the refractive power changes by 45 diopters?

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06:57

Problem 28

A converging lens of focal length 9.000 $\mathrm{cm}$ is 18.0 $\mathrm{cm}$ to the
left of a diverging lens of focal length $-6.00 \mathrm{cm} .$ A coin is placed
12.0 $\mathrm{cm}$ to the left of the converging lens. Find (a) the location
and (b) the magnification of the coin's final image.

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06:26

Problem 29

Repeat Problem $28,$ this time with the coin placed 18.0 $\mathrm{cm}$ to
the right of the diverging lens.

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01:52

Problem 30

Find the focal length of contact lenses that would allow a farsighted person with a near-point distance of 166 $\mathrm{cm}$ to read a book at a distance of 10.1 $\mathrm{cm} .$

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01:45

Problem 31

Find the focal length of contact lenses that would allow a nearsighted person with a 125 -cm far point to focus on the stars at night.

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02:00

Problem 32

What focal length should a pair of contact lenses have if they
are to correct the vision of a person with a near point of 66 $\mathrm{cm} ?$

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04:18

Problem 33

Reading glasses with a power of $+1.50$ diopters make reading a
book comfortable for you when you wear them 2.2 $\mathrm{cm}$ from your
eye. If you hold the book 28.0 $\mathrm{cm}$ your eye, what is your near-point distance?

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02:27

Problem 34

A nearsighted person wears contacts with a focal length of
$-8.5 \mathrm{cm} .$ If this person's far-point distance with her contacts is
$8.5 \mathrm{m},$ what is her uncorrected far-point distance?

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01:35

Problem 35

Without his glasses, Isaac can see objects clearly only if they are
less than 3.8 $\mathrm{m}$ from his eyes. What focal length glasses worn 2.0
$\mathrm{cm}$ from his eyes will allow Isaac to see distant objects clearly?

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03:18

Problem 36

A person whose near-point distance is 42.5 $\mathrm{cm}$ wears a pair of
glasses that are 2.1 $\mathrm{cm}$ from her eyes. With the aid of these glasses,
she can now focus on objects 25 $\mathrm{cm}$ away from her eyes. Find the
focal length and refractive power of her glasses.

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03:36

Problem 37

A pair of eyeglasses is designed to allow a person with a far-point
distance of 2.50 $\mathrm{m}$ to read a road sign at a distance of 25.0 $\mathrm{m} .$ Find
the focal length required of these glasses if they are to be worn
(a) 2.00 $\mathrm{cm}$ or ( b ) 1.00 $\mathrm{cm}$ from the eyes.

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05:21

Problem 38

Predict/Calculate Your favorite aunt can read a newspaper
only if it is within 15.0 $\mathrm{cm}$ of her eyes. (a) Is your aunt nearsighted
or farsighted? Explain. (b) Should your aunt wear glasses that are
converging or diverging to improve her vision? Explain. (c) How
many diopters of refractive power must her glasses have if they are
worn 2.00 $\mathrm{cm}$ from the eyes and allow her to read a newspaper at
a distance of 25.0 $\mathrm{cm} ?$

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04:03

Problem 39

Predict/Calculate The relaxed eyes of a patient have a refractive power of 48.5 diopters. (a) Is this patient nearsighted or farsighted? Explain. (b) If this patient is nearsighted, find the far-point. If this person is farsighted, find the near point. (For the purposes of this problem, treat the eye as a single-lens system, with the retina 2.40 $\mathrm{cm}$ from the lens.)

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05:14

Problem 40

Without glasses, your Uncle Albert can see things clearly only if
they are between 35 $\mathrm{cm}$ and 160 $\mathrm{cm}$ from his eyes.(a) What power
eyeglass lens will correct your uncle's myopia? Assume the lenses
will sit 2.0 $\mathrm{cm}$ from his eyes. (b) What is your uncle's near point
when wearing these glasses?

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07:52

Problem 41

A 2.05 -cm-tall object is placed 30.0 $\mathrm{cm}$ to the left of a converging lens with a focal length $f_{1}=20.5 \mathrm{cm} .$ A diverging lens, with
a focal length $f_{2}=-42.5 \mathrm{cm},$ is placed 30.0 $\mathrm{cm}$ to the right of the
first lens. How tall is the final image of the object?

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05:19

Problem 42

A simple camera telephoto lens consists of two lenses. The objective lens has a focallength $f_{1}=+39.0 \mathrm{cm} .$ Precisely 36.0 $\mathrm{cm}$ behind
this lens is a concave lens with a focal length $f_{2}=-10.0 \mathrm{cm} .$ The
object to be photographed is 4.00 $\mathrm{m}$ in front of the objective lens.
(a) How far behind the concave lens should the film be placed?
(b) What is the linear magnification of this lens combination?

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06:07

Problem 43

Predict/Calculate With unaided vision, a librarian can focus
only on objects that lie at distances between 5.0 $\mathrm{m}$ and 0.50 $\mathrm{m} .$
(a) Which type of lens (converging or diverging) is needed to
correct his nearsightedness? Explain. (b) Which type of lens will
correct his farsightednes? Explain. (c) Find the refractive power
needed for each part of the bifocal eyeglass lenses that will give the
librarian normal visual acuity from 25 $\mathrm{cm}$ out to infinity. (Assume
the lenses rest 2.0 $\mathrm{cm}$ from his eyes.)

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06:50

Problem 44

A person's prescription for her new bifocal glasses calls for a
refractive power of $-0.445$ diopter in the distance-vision part,
and a power of $+1.85$ diopters in the close-vision part. What
are the near and far points of this person's uncorrected vision?
Assume the glasses are 2.00 $\mathrm{cm}$ from the person's eyes, and that
the person's near-point distance is 25.0 $\mathrm{cm}$ when wearing the
glasses.

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05:49

Problem 45

A person's prescription for his new bifocal eyeglasses calls for
a refractive power of $-0.0625$ diopter in the distance-vision part
and a power of $+1.05$ diopters in the close-vision part. Assuming
the glasses rest 2.00 $\mathrm{cm}$ from his eyes and that the corrected near-point distance is $25.0 \mathrm{cm},$ determine the near and far points of this
person's uncorrected vision.

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14:39

Problem 46

Two lenses, with $f_{1}=+20.0 \mathrm{cm}$ and $f_{2}=+30.0 \mathrm{cm},$ are placed on the $x$ axis, as shown in FilsuRE $27-28 .$ An object is fixed
50.0 $\mathrm{cm}$ to the left of lens $1,$ and lens 2 is a variable distance $x$ to the right of lens $1 .$ Find the lateral magnification and location of the final image relative to lens 2 for the following cases:
(a) $x=115 \mathrm{cm} ;$ (b) $x=30.0 \mathrm{cm} ;$ (c) $x=0 .$ (d) Show that your result for part (c) agrees with the relation for the effective focal
length of two lenses in contact, $1 / f_{\text { eff }}=1 / f_{1}+1 / f_{2}$ .

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06:09

Problem 47

A converging lens with a focal length of 4.0 $\mathrm{cm}$ is to the left of
a second identical lens. When a feather is placed 12 $\mathrm{cm}$ to the left
of the first lens, the final image is the same size and orientation as
the feather itself. What is the separation between the lenses?

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03:26

Problem 48

Two magnifying glasses are for sale at a store. Magnifying
glass 1 has a 4 -in. diameter with a long focal length, and glass 2
has a 1 -in. diameter with a short focal length. (a) Which magnifying glass should you purchase if you wish to examine tiny insects?
Explain. (b) Which glass should you purchase if you wish to start a
campfire using sunlight? Explain.

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02:55

Problem 49

The Moon is 3476 $\mathrm{km}$ in diameter and orbits the Earth at an average distance of $384,400 \mathrm{km}$ . (a) What is the angular size of the
Moon as seen from Earth? (b) A penny is 19 m in diameter. How
far from your eye should the penny be held to produce the same
angular diameter as the Moon?

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04:47

Problem 50

A magnifying glass is a single convex lens with a focal length of
$f=+14.0 \mathrm{cm} .$ (a) What is the angular magnification when this
lens forms a (virtual) image at - $\infty$ ? How far from the object should
the lens be held? (b) What is the angular magnification when this
lens forms a (virtual) image at the person's near point (assumed
to be 25 $\mathrm{cm}$ )? How far from the object should the lens be held in
this case?

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01:36

Problem 51

Calculate the focal length of a magnifying lens designed to produce an angular magnification of 8.50 while producing the image at the standard near-point distance of 25.0 $\mathrm{cm} .$

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02:56

Problem 52

Predict/Calculate A student has two lenses, one of focal
length $f_{1}=5.0 \mathrm{cm}$ and the other with focal length $f_{2}=13 \mathrm{cm} .$
(a) When used as a simple magnifier, which of these lenses can produce the greater magnification? Explain. (b) Find the maximum magnification produced by each of these lenses.

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02:26

Problem 53

A beetle 4.93 $\mathrm{mm}$ long is examined with a simple magnifier of
focal length $f=10.1 \mathrm{cm} .$ If the observer's eye is relaxed while
using the magnifier, and has a near-point distance of 26.0 $\mathrm{cm},$
what is the apparent length of the beetle?

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02:45

Problem 54

To engrave wishes of good luck on a watch, an engraver uses a
magnifier whose focal length is 8.75 $\mathrm{cm} .$ If the image formed by
the magnifier is at the engraver's near point of $24.6 \mathrm{cm},$ find (a) the
distance between the watch and the magnifier and (b) the angular magnification of the engraving. Assume the magnifying glass is
directly in front of the engraver's eyes.

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01:04

Problem 55

A jeweler examines a diamond with a magnifying glass. If the
near-point distance of the jeweler is $22.8 \mathrm{cm},$ and the focal length
of the magnifying glass is $7.70 \mathrm{cm},$ find the angular magnification when the diamond is held at the focal point of the magnifier,
Assume the magnifying glass is directly in front of the jeweler's eyes.

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06:59

Problem 56

In Problem $55,$ find the angular magnification when the diamond is held 5.59 $\mathrm{cm}$ from the magnifying glass.

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02:41

Problem 57

A person with a near-point distance of 25 $\mathrm{cm}$ finds that a magnifying glass gives an angular magnification that is 1.5 times larger
when the image of the magnifier is at the near point than when
the image is at infinity. What is the focal length of the magnifying glass?

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01:22

Problem 58

You have two lenses: lens 1 with a focal length of 0.45 $\mathrm{cm}$
and lens 2 with a focal length of 1.9 $\mathrm{cm} .$ If you construct a microscope with these lenses, which one should you use as the objective? Explain.

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02:59

Problem 59

Predict/Calculate Microscope objective $A$ is labeled $15 \times$ and
objective $B$ is labeled $25 \times$ (a) Which objective has the longer focal
length? Explain. If the image formed by the objective is designed
to be 16.3 $\mathrm{cm}$ from the lens, calculate the focal length of the
(b) $15 \times$ and (c) $25 \times$ objectives.

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02:08

Problem 60

A compound microscope has an objective lens with a focal
length of 2.2 $\mathrm{cm}$ and an eyepiece with a focal length of 5.4 $\mathrm{cm} .$ If
the image produced by the objective is 12 $\mathrm{cm}$ from the objective,
what magnification does this microscope produce?

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04:24

Problem 61

A typical red blood cell subtends an angle of only
$1.9 \times 10^{-5}$ rad when viewed at a person's near-point distance of
25 $\mathrm{cm} .$ Suppose a red blood cell is examined with a compound
microscope in which the objective and eyepiece are separated by
a distance of 12.0 $\mathrm{cm} .$ Given that the focal length of the eyepiece
is $2.7 \mathrm{cm},$ and the focal length of the objective is $0.49 \mathrm{cm},$ find
the magnitude of the angle subtended by the red blood cell when
viewed through this microscope.

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03:19

Problem 62

(a) If you treat a $10 \times$ eyepiece of a microscope as a magnifying
glass that produces an image at infinity, what is its focal length? (b)
The microscope is designed for an image distance of 163 $\mathrm{mm}$ from the
objective, and the objective is marked $25 \times .$ What is its focal length?

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05:23

Problem 63

The medium-power objective lens in a laboratory microscope
has a focal length $f_{\text { objective }}=3.75 \mathrm{mm}$ . (a) If this lens produces
a magnification of $-50.0,$ what is its "working distance"; that
is, what is the distance from the object to the objective lens? (b)
What is the focal length of an eyepiece lens that will provide an
overall magnification of $-125 ?$

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03:54

Problem 64

A compound microscope has the objective and eyepiece
mounted in a tube that is 18.0 $\mathrm{cm}$ long. The focal length of the eyepiece is $2.62 \mathrm{cm},$ and the near-point distance of the person using
the microscope is 25.0 $\mathrm{cm} .$ If the person can view the image produced by the microscope with a completely relaxed eye, and the
magnification is $-4525,$ what is the focal length of the objective?

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02:40

Problem 65

The barrel of a compound microscope is 15 $\mathrm{cm}$ in length. The
specimen will be mounted 1.0 $\mathrm{cm}$ from the objective, and the eyepiece has a 5.0 -cm focal length. Determine the focal length of the objective lens.

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03:49

Problem 66

A compound microscope uses a $75.0-\mathrm{mm}$ lens as the objective
and a $2.0-\mathrm{cm}$ lens as the eyepiece. The specimen will be mounted
122 $\mathrm{mm}$ from the objective. Determine (a) the barrel length and
(b) the total magnification produced by the microscope.

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05:55

Problem 67

The "tube length" of a microscope is defined to be the difference between the (objective) image distance and objective focal length: $L=d_{1}-f_{\text { oblective }}$ . Many microscopes are standardized to a tube length of $L=160 \mathrm{mm}$ . Consider such a microscope whose
objective lens has a focal length $f_{\text { oblective }}=7.50 \mathrm{mm} .$ (a) How far
from the object should this lens be placed? (b) What focal length eyepiece would give an overall magnification of $-55 ?(\mathrm{c})$ What focal
length eyepiece would give an overall magnification of $-110 ?$

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02:33

Problem 68

Two telescopes of different lengths produce the same angular
magnification. Is the focal length of the long telescope's eyepiece
greater than or less than the focal length of the short telescope's
eyepiece? Explain.

Nathan Silvano
Nathan Silvano
Numerade Educator
01:39

Problem 69

A grade school student plans to build a 35 -power telescope as a
science fair project. She starts with a magnifying glass with a focal
length of 7.5 $\mathrm{cm}$ as the eyepiece. What focal length is needed for
her objective lens?

Nathan Silvano
Nathan Silvano
Numerade Educator
02:17

Problem 70

A 75 -power refracting telescope has an eyepiece with a focal
length of 5.0 $\mathrm{cm} .$ How long is the telescope?

Nathan Silvano
Nathan Silvano
Numerade Educator
02:14

Problem 71

An amateur astronomer wants to build a small refracting telescope. The only lenses available to him have focal lengths of $5.00 \mathrm{cm}, 10.0 \mathrm{cm}, 20.0 \mathrm{cm},$ and 30.0 $\mathrm{cm} .$ (a) What is the greatest magnification that can be obtained using two of these lenses?
(b) How long is the telescope with the greatest magnification?

Nathan Silvano
Nathan Silvano
Numerade Educator
01:29

Problem 72

A pirate sights a distant ship with a spyglass that gives an angular
magnification of $22 .$ If the focal length of the eyepiece is $11 \mathrm{mm},$
what is the focal length of the objective?

Nathan Silvano
Nathan Silvano
Numerade Educator
03:33

Problem 73

A telescope has lenses with focal lengths $f_{1}=+30.0 \mathrm{cm}$ and
$f_{2}=+5.0 \mathrm{cm} .$ (a) What distance between the two lenses will
allow the telescope to focus on an infinitely distant object and
produce an infinitely distant image? (b) What distance between the
lenses will allow the telescope to focus on an object that is 5.0 $\mathrm{m}$
away and to produce an infinitely distant image?

Nathan Silvano
Nathan Silvano
Numerade Educator
00:54

Problem 74

Jason has a 25 -power telescope whose objective lens has a focal
length of 120 $\mathrm{cm} .$ To make his sister appear smaller than normal,
he turns the telescope around and looks through the objective lens. What is the angular magnification of his sister when viewed through the "wrong" end of the telescope?

Nathan Silvano
Nathan Silvano
Numerade Educator
03:10

Problem 75

Roughing It with Science A professor shipwrecked on Hooligan's
Island decides to build a telescope from his eyeglasses and some
coconut shells. Fortunately, the professor's eyes require different
prescriptions, with the left lens having a power of $+5.0$ diopters
and the right lens having a power of $+2.0$ diopters. (a) Which lens
should he use as the objective? (b) What is the angular magnification of the professor's telescope?

Nathan Silvano
Nathan Silvano
Numerade Educator
03:01

Problem 76

Galileo's Telescope Galileo's first telescope used a convex objective lens and a concave eyepiece, as shown in FisuRE $27-29 .$ When this telescope is focused on an infinitely distant object, it produces an infinitely distant image. (a) What is the focal length of
the eyepiece of a Galilean telescope that has an objective focal
length of 1.25 $\mathrm{m}$ and a magnification of $+4.00 ?$ (b) How far apart
are the two lenses?

Nathan Silvano
Nathan Silvano
Numerade Educator
02:10

Problem 77

The Moon has an angular size of $0.50^{\circ}$ when viewed with
unaided vision from Earth. Suppose the Moon is viewed through
a telescope with an objective whose focal length is 68 $\mathrm{cm}$ and an
eyepiece whose focal length is 17 $\mathrm{mm} .$ What is the angular size of
the Moon as seen through this telescope?

Nathan Silvano
Nathan Silvano
Numerade Educator
01:49

Problem 78

A telescope is 275 $\mathrm{mm}$ long and has an objective lens with a
focal length of 257 $\mathrm{mm}$ . (a) What is the focal length of the eye-piece? (b) What is the magnification of this telescope?

Nathan Silvano
Nathan Silvano
Numerade Educator
02:18

Problem 79

The focal length for light that strikes near the center of a
spherical convex lens is 15 $\mathrm{cm} .$ Referring to Figure $27-23,$ will
the focal length for light that strikes near the edge of the lens be
greater than, less than, or equal to 15 $\mathrm{cm} ?$

Nathan Silvano
Nathan Silvano
Numerade Educator
02:04

Problem 80

The focal length for red light that strikes a spherical concave
lens is $-15 \mathrm{cm} .$ Referring to Figure $27-26,$ will the magnitude of
the (negative) focal length for blue light be greater than, less than,
or equal to 15 $\mathrm{cm} ?$

Nathan Silvano
Nathan Silvano
Numerade Educator
02:05

Problem 81

Predict/Explain Intracorneal Ring An intracorneal ring is
a small plastic device implanted in a person's cornea to change its
curvature. By changing the shape of the cornea, the intracorneal
ring can correct a person's vision. (a) If a person is nearsighted,
should the ring increase or decrease the cornea's curvature?
(b) Choose the best explanation from among the following:
I. The intracorneal ring should increase the curvature of the
cornea so that it bends light more. This will allow it to focus
on light coming from far away.
II. The intracorneal ring should decrease the curvature of the
cornea so it's flatter and bends light less. This will allow parallel rays from far away to be focused properly on the retina.

Nathan Silvano
Nathan Silvano
Numerade Educator
02:36

Problem 82

The lens in a normal human eye, with aqueous humor
on one side and vitreous humor on the other side, has a refractive
power of 15 diopters. Suppose a lens is removed from an eye and
surrounded by air. In this case, is its refractive power greater than,
less than, or equal to 15 diopters? Explain.

Nathan Silvano
Nathan Silvano
Numerade Educator
02:19

Problem 83

Predict/Explain Treating Cataracts When the lens in a person's eye becomes clouded by a cataract, the lens can be removed
with a process called phacoemulsication and replaced with a
man-made intraocular lens. The intraocular lens restores clear
vision, but its focal length cannot be changed to allow the user
to focus at different distances. In most cases, the intraocular lens
is adjusted for viewing of distant objects, and corrective glasses
are worn when viewing nearby objects. (a) Should the refractive
power of the corrective glasses be positive or negative? (b) Choose
the best explanation from among the following:
I. The refractive power should be positive - converging-
because the intraocular lens will make the person farsighted.
II. A negative refractive power is required to bring the focal point
of the intraocular lens in from infinity to a finite value.

Nathan Silvano
Nathan Silvano
Numerade Educator
06:17

Problem 84

Galileo's original telescope (Figure $27-29$ ) used a convex objective and a concave eyepiece. Use a ray diagram to show that this telescope produces an upright image when a distant object is being viewed. Assume that the eyepiece is to the right of the object and that the right-hand focal point of the eyepiece is just to the left of the objective's right-hand focal point. In addition, assume that the focal length of the eyepiece has a magnitude that is about one-quarter the focal length of the objective.

Nathan Silvano
Nathan Silvano
Numerade Educator
07:30

Problem 85

Predict/Calculate For each of the following cases, use a ray diagram to show that the angular sizes of the image and the object are identical if both angles are measured from the center of the lens. (a)A
convex lens with the object outside the focal length. (b) A convex lens with the object inside the focal length.(c) A concave lens with
the object outside the focal length. (d) Given that the angular size
does not change, how does a simple magnifier work? Explain.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
05:32

Problem 86

Predict/Calculate You have two lenses, with focal lengths
$f_{1}=+2.60 \mathrm{cm}$ and $f_{2}=+20.4 \mathrm{cm} .$ (a) How would you arrange
these lenses to form a magnified image of the Moon? (b) What is
the maximum angular magnification these lenses could produce?
(c) How would you arrange the same two lenses to form a magnified image of an insect? (d) If you use the magnifier of part (c) to view an insect, what is the angular magnification when the insect
is held 2.90 $\mathrm{cm}$ from the objective lens?

Nathan Silvano
Nathan Silvano
Numerade Educator
02:30

Problem 87

The eye is actually a multiple-lens system, but we can
approximate it with a single-lens system for most of our purposes.
When the eye is focused on a distant object, the optical power of
the equivalent single lens is $+41.4$ diopters. (a) What is the effective focal length of the eye? (b) How far in front of the retina is this "equivalent lens" located?

Nathan Silvano
Nathan Silvano
Numerade Educator
03:34

Problem 88

Fitting Contact Lenses with a Keratometer When a patient is
being fitted with contact lenses, the curvature of the patient's
cornea is measured with an instrument known as a keratometer.
A lighted object is held near the eye, and the keratometer measures the magnification of the image formed by reflection from the front of the cornea. If an object is held 10.0 $\mathrm{cm}$ in front of a
patient's eye, and the reflected image is magnified by a factor of
$0.035,$ what is the radius of curvature of the patient's cornea?

Nathan Silvano
Nathan Silvano
Numerade Educator
02:17

Problem 89

Pricey Stamp $A$ rare 1918 "Jenny" stamp, depicting a misprinted,
upside-down Curtiss JN-4 "Jenny" airplane, sold at auction for
$\$ 525,000 .$ A collector uses a simple magnifying glass to examine the
"Jenny, " obtaining a linear magnification of 2.5 when the stamp is
held 2.76 $\mathrm{cm}$ from the lens. What is the focal length of the magnifying glass?

Nathan Silvano
Nathan Silvano
Numerade Educator
02:55

Problem 90

Predict/Calculate $A$ Big Eye The largest eye ever to exist
on Earth belonged to an extinct species of ichthyosaur, Temnodontosaurus platyodon. This creature had an eye that was 26.4 $\mathrm{cm}$ in
diameter. It is estimated that this ichthyosaur also had a relatively
large pupil, giving it an effective aperture setting of about $f / 1.1 .$
(a) Assuming its pupil was one-third the diameter of the eye,
what was the approximate focal length of the ichthyosaur's eye?
(b) When the ichthyosaur narrowed its pupil in bright light, did
its $f$ -number increase or decrease? Explain.

Nathan Silvano
Nathan Silvano
Numerade Educator
02:08

Problem 91

Consider a Galilean telescope, as illustrated in Figure $27-29$ ,
constructed from two lenses with focal lengths of 75.6 $\mathrm{cm}$ and
$-18.0 \mathrm{mm} .$ (a) What is the distance between these lenses if an
infinitely distant object is to produce an infinitely distant image?
(b) What is the angular magnification when the lenses are separated by the distance calculated in part (a)?

Nathan Silvano
Nathan Silvano
Numerade Educator
03:17

Problem 92

A farsighted person uses glasses with a refractive power of 3.6
diopters. The glasses are worn 2.5 $\mathrm{cm}$ from his eyes. What is this
person's near point when not wearing glasses?

Nathan Silvano
Nathan Silvano
Numerade Educator
03:55

Problem 93

Landing on an Aircraft Carrier The Fresnel Lens Optical Landing
System (FLOLS) used to ensure safe landings on aircraft carriers consists of a series of Fresnel lenses of different colors. Each lens focuses light in a different, specific direction, and hence which light a pilot
sees on approach determines whether the plane is above, below, or
on the proper landing path. The basic idea behind a Fresnel lens,
which has the same optical properties as an ordinary lens, is shown
in FIGURE $27-30 .$ Suppose an object is 17.1 $\mathrm{cm}$ behind a Fresnel lens,
and that the corresponding image is a distance $d_{1}=d$ in front of the
lens. If the object is moved to a distance of 12.0 $\mathrm{cm}$ behind the lens,
the image distance doubles to $d_{1}=2 d .$ In the FLOLS, it is desired
to have the image of the light bulb at infinity. What object distance
will give this result for this particular lens?

Nathan Silvano
Nathan Silvano
Numerade Educator
03:41

Problem 94

A Cassegrain astronomical telescope uses two mirrors to form
the image. The larger (concave) objective mirror has a focal length
$f_{1}=+50.0 \mathrm{cm} .$ A small convex secondary mirror is mounted
43.0 $\mathrm{cm}$ in front of the primary. As shown in FlGURE $27-31,$ light is
reflected from the secondary through a hole in the center of the
primary, thereby forming a real image 8.00 $\mathrm{cm}$ behind the primary
mirror. What is the radius of curvature of the secondary mirror?

Nathan Silvano
Nathan Silvano
Numerade Educator
05:59

Problem 95

Predict/Calculate A convex lens $(f=20.0 \mathrm{cm})$ is placed
10.0 $\mathrm{cm}$ in front of a plane mirror. A matchstick is placed 25.0 $\mathrm{cm}$
in front of the lens, as shown in FlGURE $27-32$ . (a) If you lookthrough
the lens toward the mirror, where will you see the image of the
matchstick? Is the image real or virtual? Explain. (c) What is the
magnification of the image? (d) Is the image upright or inverted?

Nathan Silvano
Nathan Silvano
Numerade Educator
01:58

Problem 96

The diameter of a collimated laser beam can be expanded or
reduced by using two converging lenses, with focal lengths $f_{1}$
and $f_{2},$ mounted a distance $f_{1}+f_{2}$ from each other, as shown in
FIGURE $27-33 .$ What is the ratio of the two beam diameters, $\left(d_{1} / d_{2}\right)$
expressed in terms of the focal lengths?

Nathan Silvano
Nathan Silvano
Numerade Educator
09:06

Problem 97

Consider three lenses with focal lengths of $25.0 \mathrm{cm},-15.0 \mathrm{cm},$
and 11.0 $\mathrm{cm}$ positioned on the $x$ axis at $x=0, x=0.400 \mathrm{m},$ and
$x=0.500 \mathrm{m},$ respectively. An object is at $x=-122 \mathrm{cm} .$ Find (a) the

Nathan Silvano
Nathan Silvano
Numerade Educator
05:19

Problem 98

Because a concave lens cannot form a real image of a real
object, it is difficult to measure its focal length precisely. One
method uses a second, convex, lens to produce a virtual object for
the concave lens. Under the proper conditions, the concave lens
will form a real image of the virtual object! A student conducting
a laboratory project on concave lenses makes the following observations: When a lamp is placed 42.0 $\mathrm{cm}$ to the left of a particular
convex lens, a real (inverted) image is formed 37.5 $\mathrm{cm}$ to the right
of the lens. The lamp and convex lens are kept in place while a
concave lens is mounted 15.0 $\mathrm{cm}$ to the right of the convex lens.
A real image of the lamp is now formed 35.0 $\mathrm{cm}$ to the right of the
concave lens. What is the focal length of each lens?

Nathan Silvano
Nathan Silvano
Numerade Educator
02:33

Problem 99

A person with a near-point distance $N$ uses a magnifying glass
with a focal length $f$ . Show that the greatest magnification that
can be achieved with this magnifier is $M=1+N / f$ .

Nathan Silvano
Nathan Silvano
Numerade Educator
02:10

Problem 100

Cataracts and Intraocular Lenses
A cataract is an opacity or "cloudiness" that develops in the lens
of an eye. The result can be serious degradation of vision, or even
blindness. Cataracts can be caused by prolonged exposure to electromagnetic radiation of almost any form. For example, cataracts
are unusually common among airline pilots, who encounter intense UV exposure at high altitude. To delay cataract formation,
doctors recommend protecting the eyes from sunlight with sun-glasses or a hat with a brim.
Cataracts are generally treated by removing the affected lens with
a technique referred to as phacoemulsification. After the natural lens
is removed, it is replaced with a man-made, intraocular lens, or IOL.
In many cases, the IOL is rigid; neither its focal length nor location
can be changed. In most cases these lenses are designed to allow the
eye to see clearly at infinity, but corrective glasses or contacts must be
worn for close vision. In extreme cases, a "piggyback" IOL may need
to be installed along with the original IOL to fine-tune the optics.
More recently, adaptive IOLs have been developed that flex
when the focusing muscles of the eye contract, thus allowing a degree of accommodation. This is illustrated in FlisuRE $27-34,$ where we see the IOL move forward to focus on a close object. Notice that the focal length of the adaptive IOL is fixed, just as with a normal
IOL, but the eye muscles can change its location- the same as in a
camera when it focuses.
A patient receives a rigid IOL whose focus cannot be changed
it is designed to provide clear vision of objects at infinity. The
patient will use corrective contacts to allow for close vision.
Should the refractive power of the corrective contacts be positive
or negative?

Nathan Silvano
Nathan Silvano
Numerade Educator
02:28

Problem 101

Cataracts and Intraocular Lenses
A cataract is an opacity or "cloudiness" that develops in the lens
of an eye. The result can be serious degradation of vision, or even
blindness. Cataracts can be caused by prolonged exposure to electromagnetic radiation of almost any form. For example, cataracts
are unusually common among airline pilots, who encounter intense UV exposure at high altitude. To delay cataract formation,
doctors recommend protecting the eyes from sunlight with sun-glasses or a hat with a brim.
Cataracts are generally treated by removing the affected lens with
a technique referred to as phacoemulsification. After the natural lens
is removed, it is replaced with a man-made, intraocular lens, or IOL.
In many cases, the IOL is rigid; neither its focal length nor location
can be changed. In most cases these lenses are designed to allow the
eye to see clearly at infinity, but corrective glasses or contacts must be
worn for close vision. In extreme cases, a "piggyback" IOL may need
to be installed along with the original IOL to fine-tune the optics.
More recently, adaptive IOLs have been developed that flex
when the focusing muscles of the eye contract, thus allowing a degree of accommodation. This is illustrated in FlisuRE $27-34,$ where we see the IOL move forward to focus on a close object. Notice that the focal length of the adaptive IOL is fixed, just as with a normal
IOL, but the eye muscles can change its location- the same as in a
camera when it focuses.
Referring to the previous problem, find the refractive power of
contacts that will allow the patient to focus on a book at a distance of 23.0 $\mathrm{cm} .$
$$
\begin{array}{ll}{\text { A. } 0.0435 \text { diopter }} & {\text { B. } 0.230 \text { diopter }} \\ {\text { C. } 4.35 \text { diopters }} & {\text { D. } 8.70 \text { diopters }}\end{array}
$$

Nathan Silvano
Nathan Silvano
Numerade Educator
01:59

Problem 102

Cataracts and Intraocular Lenses
A cataract is an opacity or "cloudiness" that develops in the lens
of an eye. The result can be serious degradation of vision, or even
blindness. Cataracts can be caused by prolonged exposure to electromagnetic radiation of almost any form. For example, cataracts
are unusually common among airline pilots, who encounter intense UV exposure at high altitude. To delay cataract formation,
doctors recommend protecting the eyes from sunlight with sun-glasses or a hat with a brim.
Cataracts are generally treated by removing the affected lens with
a technique referred to as phacoemulsification. After the natural lens
is removed, it is replaced with a man-made, intraocular lens, or IOL.
In many cases, the IOL is rigid; neither its focal length nor location
can be changed. In most cases these lenses are designed to allow the
eye to see clearly at infinity, but corrective glasses or contacts must be
worn for close vision. In extreme cases, a "piggyback" IOL may need
to be installed along with the original IOL to fine-tune the optics.
More recently, adaptive IOLs have been developed that flex
when the focusing muscles of the eye contract, thus allowing a degree of accommodation. This is illustrated in FlisuRE $27-34,$ where we see the IOL move forward to focus on a close object. Notice that the focal length of the adaptive IOL is fixed, just as with a normal
IOL, but the eye muscles can change its location- the same as in a
camera when it focuses.
After a fixed IOL is installed, it is found to have the wrong
focal length, so a piggyback IOL is installed as well. The piggy-back IOL has a power of -1.50 diopters. What is its focal length
and type?
$$
\begin{array}{ll}{\text { A. converging, } 1.50 \mathrm{m}} & {\text { B. converging, } 66.7 \mathrm{cm}} \\ {\text { C. diverging, } 1.50 \mathrm{m}} & {\text { D. diverging, } 66.7 \mathrm{cm}}\end{array}
$$

Nathan Silvano
Nathan Silvano
Numerade Educator
03:27

Problem 103

Cataracts and Intraocular Lenses
A cataract is an opacity or "cloudiness" that develops in the lens
of an eye. The result can be serious degradation of vision, or even
blindness. Cataracts can be caused by prolonged exposure to electromagnetic radiation of almost any form. For example, cataracts
are unusually common among airline pilots, who encounter intense UV exposure at high altitude. To delay cataract formation,
doctors recommend protecting the eyes from sunlight with sun-glasses or a hat with a brim.
Cataracts are generally treated by removing the affected lens with
a technique referred to as phacoemulsification. After the natural lens
is removed, it is replaced with a man-made, intraocular lens, or IOL.
In many cases, the IOL is rigid; neither its focal length nor location
can be changed. In most cases these lenses are designed to allow the
eye to see clearly at infinity, but corrective glasses or contacts must be
worn for close vision. In extreme cases, a "piggyback" IOL may need
to be installed along with the original IOL to fine-tune the optics.
More recently, adaptive IOLs have been developed that flex
when the focusing muscles of the eye contract, thus allowing a degree of accommodation. This is illustrated in FlisuRE $27-34,$ where we see the IOL move forward to focus on a close object. Notice that the focal length of the adaptive IOL is fixed, just as with a normal
IOL, but the eye muscles can change its location- the same as in a
camera when it focuses.
Suppose a flexible, adaptive IOL has a focal length of 3.00 $\mathrm{cm}$ .
How far forward must the IOL move to change the focus of the eye
from an object at infinity to an object at a distance of 50.0 $\mathrm{cm} ?$
$$
\begin{array}{ll}{\text { A. } 1.9 \mathrm{mm}} & {\text { B. } 2.8 \mathrm{mm}} \\ {\text { C. } 3.1 \mathrm{mm}} & {\text { D. } 3.2 \mathrm{mm}}\end{array}
$$

Nathan Silvano
Nathan Silvano
Numerade Educator
03:11

Problem 104

Predict/Calculate REFERING TO EXAMPIE $27-4$ Suppose a person's
eyeglasses have a focal length of $-301 \mathrm{cm},$ are 2.00 $\mathrm{cm}$ in front of
the eyes, and allow the person to focus on distant objects. (a) Is this person's far point greater than or less than $323 \mathrm{cm},$ which is the far
point for glasses the same distance from the eyes and with a focal
length of $-321 \mathrm{cm} ?$ Explain. (b) Find the far point for this person.

Nathan Silvano
Nathan Silvano
Numerade Educator
04:25

Problem 105

Predict/Calculate REFERING TO EXAMPLE $27-4$ In Example $27-$
$4,$ a person has a far-point distance of 323 $\mathrm{cm} .$ If this person
wears glasses 2.00 $\mathrm{cm}$ in front of the eyes with a focal length of
$-321 \mathrm{cm},$ distant objects can be brought into focus. Suppose a
second person's far point is 353 $\mathrm{cm} .$ (a) Is the magnitude of the
focal length of the eyeglasses that allow this person to focus on
distant objects greater than or less than 321 $\mathrm{cm} ?$ Assume the
glasses are 2.00 $\mathrm{cm}$ in front of the eyes. (b) Find the required focal
length for the second person's eyeglasses.

Nathan Silvano
Nathan Silvano
Numerade Educator
03:51

Problem 106

Predict/Calculate REFERING TO EXAMPLE $27-6$ Suppose a person's
eyeglasses have a refractive power of 2.75 diopters and that they
allow the person to focus on an object that is just 25.0 $\mathrm{cm}$ from
the eye. The glasses are 2.00 $\mathrm{cm}$ in front of the eyes. (a) Is this person's near point greater than or less than $57.0 \mathrm{cm},$ which is
the near-point distance when the glasses have a refractive power
of 2.53 diopters? Explain. (b) Find the near point for this person.

Nathan Silvano
Nathan Silvano
Numerade Educator
04:40

Problem 107

Predict/Calculate REfERING TO EXAMPLE $27-6$ Suppose a person's
near-point distance is 67.0 $\mathrm{cm} .$ (a) Is the refractive power of the
eyeglasses that allow this person to focus on an object just 25.0 $\mathrm{cm}$
from the eye greater than or less than 2.53 diopters, which is the
refractive power when the near-point distance is 57.0 $\mathrm{cm} ?$ The
glasses are worn 2.00 $\mathrm{cm}$ in front of the eyes. (b) Find the required
refractive power for this person's eyeglasses.

Nathan Silvano
Nathan Silvano
Numerade Educator