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Physics: Principles with Applications

Douglas C. Giancoli

Chapter 25

OPTICAL INSTRUMENTS - all with Video Answers

Educators


Chapter Questions

02:53

Problem 1

(I) A properly exposed photograph is taken at $f$/ 16 and ${1\over100}$s. What lens opening is required if the shutter speed is ${1\over400}$s?

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00:46

Problem 2

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

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01:44

Problem 3

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

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02:51

Problem 4

(I) A light meter reports that a camera setting of ${1\over500}$s at $f$/ 5.6 will give a correct exposure. But the photographer wishes to use $f$/11 to increase the depth of field. What should the shutter speed be?

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02:24

Problem 5

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

Abhishek Jana
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02:08

Problem 6

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

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03:58

Problem 7

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

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04:03

Problem 8

(II) How large is the image of the Sun on film used in a camera with ($a$) a 28-mm-focal-length lens, ($b$) a 50-mm-focal- length lens, and ($c$) a 135-mm-focal-length lens? ($d$) If
the 50-mm lens is considered normal for this camera, what relative magnification does each of the other two lenses provide? The Sun has diameter 1.4 $\times$ 10$^6$ km, and it is 1.5 $\times$ 10$^8$ km away.

Abhishek Jana
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04:07

Problem 9

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

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01:18

Problem 10

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

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01:07

Problem 11

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

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02:42

Problem 12

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

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02:49

Problem 13

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

Abhishek Jana
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04:44

Problem 14

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

Abhishek Jana
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03:51

Problem 15

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

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01:58

Problem 16

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

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03:19

Problem 17

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

Abhishek Jana
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04:17

Problem 18

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

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02:27

Problem 19

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

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02:29

Problem 20

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

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04:17

Problem 21

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

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00:54

Problem 22

(I) What is the focal length of a magnifying glass of 3.2$\times$ magnification for a relaxed normal eye?

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00:43

Problem 23

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

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01:28

Problem 24

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

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02:54

Problem 25

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

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02:25

Problem 26

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

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05:02

Problem 27

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

Abhishek Jana
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01:46

Problem 28

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

Abhishek Jana
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06:10

Problem 29

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

Abhishek Jana
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01:38

Problem 30

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

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01:20

Problem 31

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

Abhishek Jana
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02:19

Problem 32

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

Abhishek Jana
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01:18

Problem 33

(II) A 7.0$\times$ binocular has 3.5-cm-focal-length eyepieces. What is the focal length of the objective lenses?

Abhishek Jana
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01:28

Problem 34

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

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03:16

Problem 35

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

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01:42

Problem 36

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

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01:41

Problem 37

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

Abhishek Jana
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01:46

Problem 38

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

Abhishek Jana
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05:02

Problem 39

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

Abhishek Jana
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02:02

Problem 40

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

Abhishek Jana
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04:58

Problem 41

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

Abhishek Jana
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04:14

Problem 42

(III) A pair of 6.5$\times$ binoculars has an objective focal length of 26 cm. If the binoculars are focused on an object 4.0 m away (from the objective), what is the magnification?
(The 6.5$\times$ refers to objects at infinity; Eq. 25$-$3 holds only for objects at infinity and not for nearby ones.)

Abhishek Jana
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01:12

Problem 43

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

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01:52

Problem 44

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

Abhishek Jana
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00:46

Problem 45

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

Abhishek Jana
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07:34

Problem 46

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

Abhishek Jana
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09:25

Problem 47

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

Abhishek Jana
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04:30

Problem 48

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

Abhishek Jana
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03:24

Problem 49

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

Supratim Pal
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04:40

Problem 50

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

Abhishek Jana
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02:16

Problem 51

(II) An achromatic lens is made of two very thin lenses, placed in contact, that have focal lengths $f_1=-27.8$ cm and $f_2=+$25.3 cm ($a$) Is the combination converging or diverging? ($b$) What is the net focal length?

Abhishek Jana
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05:12

Problem 52

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

Abhishek Jana
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02:02

Problem 53

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

Abhishek Jana
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01:22

Problem 54

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

Abhishek Jana
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02:38

Problem 55

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

Abhishek Jana
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05:17

Problem 56

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

Abhishek Jana
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02:08

Problem 57

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

Abhishek Jana
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03:44

Problem 58

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

Abhishek Jana
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04:09

Problem 59

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

Abhishek Jana
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01:14

Problem 60

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

Abhishek Jana
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03:18

Problem 61

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

Abhishek Jana
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02:20

Problem 62

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

Abhishek Jana
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03:20

Problem 63

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

Abhishek Jana
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06:29

Problem 64

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

Abhishek Jana
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04:26

Problem 65

Suppose that a correct exposure is $1\over250$s at $f /$11. Under the same conditions, what exposure time would be needed for a $pinhole$ camera (Problem 64) if the pinhole diameter is 1.0 mm and the film is 7.0 cm from the hole?

Abhishek Jana
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03:19

Problem 66

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

Abhishek Jana
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05:12

Problem 67

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

Abhishek Jana
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03:26

Problem 68

Figure 25$-$48 was taken from the NIST Laboratory (National Institute of Standards and Technology) in Boulder, CO, 2.0 km from the hiker in the photo. The Sun's image was 15 mm across on the film. Estimate the focal length of the camera lens (actually a telescope). The Sun has diameter 1.4 $\times$10$^6$ km, and it is 1.5 $\times$10$^8$ km away.
FIGURE 25–48 Problem 68. (FIGURE CAN'T COPY)

Abhishek Jana
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01:34

Problem 69

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

Abhishek Jana
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03:25

Problem 70

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

Abhishek Jana
Abhishek Jana
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02:21

Problem 71

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

Abhishek Jana
Abhishek Jana
Numerade Educator
02:02

Problem 72

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

Abhishek Jana
Abhishek Jana
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04:02

Problem 73

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

Abhishek Jana
Abhishek Jana
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01:09

Problem 74

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

Abhishek Jana
Abhishek Jana
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01:35

Problem 75

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

Abhishek Jana
Abhishek Jana
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00:43

Problem 76

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

Abhishek Jana
Abhishek Jana
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03:40

Problem 77

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

Abhishek Jana
Abhishek Jana
Numerade Educator
03:57

Problem 78

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

Abhishek Jana
Abhishek Jana
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03:00

Problem 79

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

Abhishek Jana
Abhishek Jana
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03:27

Problem 80

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

Abhishek Jana
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02:04

Problem 81

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

Abhishek Jana
Abhishek Jana
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04:47

Problem 82

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

Abhishek Jana
Abhishek Jana
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02:13

Problem 83

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

Abhishek Jana
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01:28

Problem 84

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

Abhishek Jana
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02:22

Problem 85

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

Abhishek Jana
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02:20

Problem 86

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

Abhishek Jana
Abhishek Jana
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02:10

Problem 87

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

Abhishek Jana
Abhishek Jana
Numerade Educator
05:18

Problem 88

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

Abhishek Jana
Abhishek Jana
Numerade Educator
02:19

Problem 89

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

Abhishek Jana
Abhishek Jana
Numerade Educator