University Physics

Samuel J. Ling, Jeff Sanny, William Moebs

Chapter 1 The Nature of Light - all with Video Answers

Educators

Chapter Questions

02:27

Problem 1

Under what conditions can light be modeled like a ray? Like a wave?

Brianna Owen

Numerade Educator

01:01

Problem 2

Why is the index of refraction always greater than or equal to $1 ?$

Brianna Owen

Numerade Educator

02:56

Does the fact that the light flash from lightning reaches you before its sound prove that the speed of light is extremely large or simply that it is greater than the speed of sound? Discuss how you could use this effect to get an estimate of the speed of light.

Brianna Owen

Numerade Educator

01:10

Problem 4

Speculate as to what physical process might be responsible for light traveling more slowly in a medium than in a vacuum.

Mayukh Banik

Numerade Educator

01:01

Problem 5

Using the law of reflection, explain how powder takes the shine off of a person's nose. What is the name of the optical effect?

Brianna Owen

Numerade Educator

01:02

Problem 6

Diffusion by reflection from a rough surface is described in this chapter. Light can also be diffused by refraction. Describe how this occurs in a specific situation, such as light interacting with crushed ice.

Mayukh Banik

Numerade Educator

01:07

Problem 7

Will light change direction toward or away from the perpendicular when it goes from air to water? Water to glass? Glass to air?

Mayukh Banik

Numerade Educator

01:05

Problem 8

Explain why an object in water always appears to be at a depth shallower than it actually is?

Mayukh Banik

Numerade Educator

00:50

Problem 9

Explain why a person's legs appear very short when wading in a pool. Justify your explanation with a ray diagram showing the path of rays from the feet to the eye of an observer who is out of the water.

Mayukh Banik

Numerade Educator

01:24

Problem 10

Explain why an oar that is partially submerged in water appears bent.

Mayukh Banik

Numerade Educator

01:09

Problem 11

A ring with a colorless gemstone is dropped into water. The gemstone becomes invisible when submerged. Can it be a diamond? Explain.

Mayukh Banik

Numerade Educator

01:43

Problem 12

The most common type of mirage is an illusion that light from faraway objects is reflected by a pool of water that is not really there. Mirages are generally observed in deserts, when there is a hot layer of air near the ground. Given that the refractive index of air is lower for air at higher temperatures, explain how mirages can be formed.

Mayukh Banik

Numerade Educator

01:15

Problem 13

How can you use total internal reflection to estimate the index of refraction of a medium?

Mayukh Banik

Numerade Educator

00:56

Problem 14

Is it possible that total internal reflection plays a role in rainbows? Explain in tems of indices of refraction and angles, perhaps referring to that shown below. Some of us have seen the formation of a double rainbow; is it physically possible to observe a triple rainbow?

Mayukh Banik

Numerade Educator

01:28

Problem 15

A high-quality diamond may be quite clear and colorless, transmitting all visible wavelengths with little absorption. Explain how it can sparkle with flashes of brilliant color when illuminated by white light.

Mayukh Banik

Numerade Educator

01:16

Problem 16

How do wave effects depend on the size of the object with which the wave interacts? For example, why does sound bend around the comer of a building while light does not?

Mayukh Banik

Numerade Educator

00:48

Problem 17

Does Huygens's principle apply to all types of waves?

Mayukh Banik

Numerade Educator

00:33

Problem 18

If diffraction is observed for some phenomenon, it is evidence that the phenomenon is a wave. Does the reverse hold true? That is, if diffraction is not observed, does that mean the phenomenon is not a wave?

Mayukh Banik

Numerade Educator

00:37

Problem 19

Can a sound wave in air be polarized? Explain.

Mayukh Banik

Numerade Educator

01:16

Problem 20

No light passes through two perfect polarizing filters with perpendicular axes. However, if a third polarizing filter is placed between the original two, some light can pass. Why is this? Under what circumstances does most of the light pass?

Mayukh Banik

Numerade Educator

01:00

Problem 21

Explain what happens to the energy carried by light that it is dimmed by passing it through two crossed polarizing filters.

Mayukh Banik

Numerade Educator

01:58

Problem 22

When particles scattering light are much smaller than its wavelength, the amount of scattering is proportional to $\frac{1}{\lambda} .$ Does this mean there is more scattering for small $\lambda$ than large $\lambda$ ? How does this relate to the fact that the sky is blue?

Brianna Owen

Numerade Educator

00:55

Problem 23

Using the information given in the preceding question, explain why sunsets are red.

Mayukh Banik

Numerade Educator

01:06

Problem 24

When light is reflected at Brewster's angle from a smooth surface, it is $100 \%$ polarized parallel to the surface. Part of the light will be refracted into the surface. Describe how you would do an experiment to determine the polarization of the refracted light. What direction would you expect the polarization to have and would you expect it to be $100 \%$ ?

Mayukh Banik

Numerade Educator

01:13

Problem 25

If you lie on a beach looking at the water with your head tipped slightly sideways, your polarized sunglasses do not work very well. Why not?

Brianna Owen

Numerade Educator

01:32

Problem 26

What is the speed of light in water? In glycerine?

Salamat Ali

Numerade Educator

01:45

Problem 27

What is the speed of light in air? In crown glass?

Salamat Ali

Numerade Educator

00:41

Problem 28

Calculate the index of refraction for a medium in which the speed of light is $2.012 \times 10^{8} \mathrm{m} / \mathrm{s},$ and identify the most likely substance based on Table 1.1.

Mayukh Banik

Numerade Educator

00:38

Problem 29

In what substance in Table 1.1 is the speed of light $2.290 \times 10^{8} \mathrm{m} / \mathrm{s} ?$

Mayukh Banik

Numerade Educator

00:41

Problem 30

There was a major collision of an asteroid with the Moon in medieval times. It was described by monks at Canterbury Cathedral in England as a red glow on and around the Moon. How long after the asteroid hit the Moon, which is $3.84 \times 10^{5} \mathrm{km}$ away, would the light first arrive on Earth?

Salamat Ali

Numerade Educator

00:59

Problem 31

Components of some computers communicate with each other through optical fibers having an index of refraction $n=1.55 .$ What time in nanoseconds is required for a signal to travel $0.200 \mathrm{m}$ through such a fiber?

Salamat Ali

Numerade Educator

02:10

Problem 32

Compare the time it takes for light to travel $1000 \mathrm{m}$ on the surface of Earth and in outer space.

Mayukh Banik

Numerade Educator

00:47

Problem 33

How far does light travel underwater during a time interval of $1.50 \times 10^{-6} \mathrm{s} ?$

Mayukh Banik

Numerade Educator

02:12

Problem 34

Suppose a man stands in front of a mirror as shown below. His eyes are $1.65 \mathrm{m}$ above the floor and the top of his head is $0.13 \mathrm{m}$ higher. Find the height above the floor of the top and bottom of the smallest mirror in which he can see both the top of his head and his feet. How is this distance related to the man's height?

Mayukh Banik

Numerade Educator

00:56

Problem 35

Show that when light reflects from two mirrors that meet each other at a right angle, the outgoing ray is parallel to the incoming ray, as illustrated below.

Brianna Owen

Numerade Educator

03:14

Problem 36

On the Moon's surface, lunar astronauts placed a comer reflector, off which a laser beam is periodically reflected. The distance to the Moon is calculated from the round-trip time. What percent correction is needed to account for the delay in time due to the slowing of light in Earth's atmosphere? Assume the distance to the Moon is precisely $3.84 \times 10^{8} \mathrm{m}$ and Earth's atmosphere (which varies in density with altitude) is equivalent to a layer $n=1.000293$.

Mayukh Banik

Numerade Educator

01:24

Problem 37

A flat mirror is neither converging nor diverging. To prove this, consider two rays originating from the same point and diverging at an angle $\theta$ (see below). Show that after striking a plane mirror, the angle between their directions remains $\theta$.
Unless otherwise specified, for problems 1 through $10,$ the indices of refraction of glass and water should be taken to be 1.50 and $1.333,$ respectively.

Mayukh Banik

Numerade Educator

01:16

Problem 38

A light beam in air has an angle of incidence of $35^{\circ}$ at the surface of a glass plate. What are the angles of reflection and refraction?

Mayukh Banik

Numerade Educator

00:54

Problem 39

A light beam in air is incident on the surface of a pond, making an angle of $20^{\circ}$ with respect to the surface. What are the angles of reflection and refraction?

Mayukh Banik

Numerade Educator

01:03

Problem 40

When a light ray crosses from water into glass, it emerges at an angle of $30^{\circ}$ with respect to the normal of the interface. What is its angle of incidence?

Mayukh Banik

Numerade Educator

00:45

Problem 41

A pencil flashlight submerged in water sends a light beam toward the surface at an angle of incidence of $30^{\circ}$. What is the angle of refraction in air?

Mayukh Banik

Numerade Educator

00:41

Problem 42

Light rays from the Sun make a $30^{\circ}$ angle to the vertical when seen from below the surface of a body of water. At what angle above the horizon is the Sun?

Mayukh Banik

Numerade Educator

00:48

Problem 43

The path of a light beam in air goes from an angle of incidence of $35^{\circ}$ to an angle of refraction of $22^{\circ}$ when it enters a rectangular block of plastic. What is the index of refraction of the plastic?

Mayukh Banik

Numerade Educator

00:45

Problem 44

A scuba diver training in a pool looks at his instructor as shown below. What angle does the ray from the instructor's face make with the perpendicular to the water at the point where the ray enters? The angle between the ray in the water and the perpendicular to the water is $25.0^{\circ}$.

Mayukh Banik

Numerade Educator

02:22

Problem 45

(a) Using information in the preceding problem, find the height of the instructor's head above the water, noting that you will first have to calculate the angle of incidence.
(b) Find the apparent depth of the diver's head below water as seen by the instructor.

Mayukh Banik

Numerade Educator

01:17

Problem 46

Verify that the critical angle for light going from water to air is $48.6^{\circ},$ as discussed at the end of Example 1.4 regarding the critical angle for light traveling in a polystyrene (a type of plastic) pipe surrounded by air.

Salamat Ali

Numerade Educator

01:42

Problem 47

(a) At the end of Example $1.4,$ it was stated that the critical angle for light going from diamond to air is $24.4^{\circ}.$ Verify this. (b) What is the critical angle for light going from zircon to air?

Salamat Ali

Numerade Educator

01:04

Problem 48

An optical fiber uses flint glass clad with crown glass. What is the critical angle?

Narayan Hari

Numerade Educator

01:11

Problem 49

At what minimum angle will you get total internal reflection of light traveling in water and reflected from ice?

Salamat Ali

Numerade Educator

00:53

Problem 50

Suppose you are using total internal reflection to make an efficient corner reflector. If there is air outside and the incident angle is $45.0^{\circ},$ what must be the minimum index of refraction of the material from which the reflector is made?

Salamat Ali

Numerade Educator

01:24

Problem 51

You can determine the index of refraction of a substance by determining its critical angle. (a) What is the index of refraction of a substance that has a critical angle of $68.4^{\circ}$ when submerged in water? What is the substance, based on Table $1.1 ?$ (b) What would the critical angle be for this substance in air?

Mayukh Banik

Numerade Educator

02:16

Problem 52

A ray of light, emitted beneath the surface of an unknown liquid with air above it, undergoes total internal reflection as shown below. What is the index of refraction for the liquid and its likely identification?

Mayukh Banik

Numerade Educator

01:10

Problem 53

Light rays fall normally on the vertical surface of the glass prism $(n=1.50)$ shown below. (a) What is the largest value for $\phi$ such that the ray is totally reflected at the slanted face? (b) Repeat the calculation of part (a) if the prism is immersed in water.

Mayukh Banik

Numerade Educator

01:24

Problem 54

(a) What is the ratio of the speed of red light to violet light in diamond, based on Table $1.2 ?$ (b) What is this ratio in polystyrene? (c) Which is more dispersive?

Mayukh Banik

Numerade Educator

01:17

Problem 55

A beam of white light goes from air into water at an incident angle of $75.0^{\circ} .$ At what angles are the red (660 nm) and violet (410 nm) parts of the light refracted?

Salamat Ali

Numerade Educator

01:39

Problem 56

By how much do the critical angles for red (660 nm) and violet (410 nm) light differ in a diamond surrounded by air?

Salamat Ali

Numerade Educator

02:25

Problem 57

(a) A narrow beam of light containing yellow (580 nm) and green (550 nm) wavelengths goes from polystyrene to air, striking the surface at a $30.0^{\circ}$ incident angle. What is the angle between the colors when they emerge? (b) How far would they have to travel to be separated by $1.00 \mathrm{mm}$ ?

Salamat Ali

Numerade Educator

03:13

Problem 58

A parallel beam of light containing orange (610 nm) and violet (410 nm) wavelengths goes from fused quartz to water, striking the surface between them at a $60.0^{\circ}$ incident angle. What is the angle between the two colors in water?

Salamat Ali

Numerade Educator

01:33

Problem 59

A ray of 610 -nm light goes from air into fused quartz at an incident angle of $55.0^{\circ} .$ At what incident angle must $470 \mathrm{nm}$ light enter flint glass to have the same angle of refraction?

Salamat Ali

Numerade Educator

04:08

Problem 60

A narrow beam of light containing red (660 nm) and blue $(470 \mathrm{nm})$ wavelengths travels from air through a $1.00-\mathrm{cm}$ -thick flat piece of crown glass and back to air again. The beam strikes at a $30.0^{\circ}$ incident angle. (a) $\mathrm{At}$ what angles do the two colors emerge? (b) By what distance are the red and blue separated when they emerge?

Mayukh Banik

Numerade Educator

04:45

Problem 61

A narrow beam of white light enters a prism made of crown glass at a $45.0^{\circ}$ incident angle, as shown below. At what angles, $\theta_{\mathrm{R}}$ and $\theta_{\mathrm{V}},$ do the red $(660 \mathrm{nm})$ and violet
(410 nm) components of the light emerge from the prism?

Mayukh Banik

Numerade Educator

00:34

Problem 62

What angle is needed between the direction of polarized light and the axis of a polarizing filter to cut its intensity in half?

Salamat Ali

Numerade Educator

View

Problem 63

The angle between the axes of two polarizing filters is $45.0^{\circ} .$ By how much does the second filter reduce the intensity of the light coming through the first?

Ankur S

Numerade Educator

00:29

Problem 64

Two polarizing sheets $P_{1}$ and $P_{2}$ are placed together with their transmission axes oriented at an angle $\theta$ to each other. What is $\theta$ when only $25 \%$ of the maximum transmitted light intensity passes through them?

Mayukh Banik

Numerade Educator

00:52

Problem 65

Suppose that in the preceding problem the light incident on $P_{1}$ is unpolarized. At the determined value of $\theta,$ what fraction of the incident light passes through the combination?

Mayukh Banik

Numerade Educator

00:41

Problem 66

If you have completely polarized light of intensity $150 \mathrm{W} / \mathrm{m}^{2},$ what will its intensity be after passing through a polarizing filter with its axis at an $89.0^{\circ}$ angle to the light's polarization direction?

Mayukh Banik

Numerade Educator

00:57

Problem 67

What angle would the axis of a polarizing filter need to make with the direction of polarized light of intensity $1.00 \mathrm{kW} / \mathrm{m}^{2}$ to reduce the intensity to $10.0 \mathrm{W} / \mathrm{m}^{2} ?$

Salamat Ali

Numerade Educator

01:31

Problem 68

At the end of Example $1.7,$ it was stated that the intensity of polarized light is reduced to $90.0 \%$ of its original value by passing through a polarizing filter with its axis at an angle of $18.4^{\circ}$ to the direction of polarization. Verify this statement.

Salamat Ali

Numerade Educator

01:28

Problem 69

Show that if you have three polarizing filters, with the second at an angle of $45.0^{\circ}$ to the first and the third at an angle of $90.0^{\circ}$ to the first, the intensity of light passed by the first will be reduced to $25.0 \%$ of its value. (This is in contrast to having only the first and third, which reduces the intensity to zero, so that placing the second between them increases the intensity of the transmitted light.)

Mayukh Banik

Numerade Educator

01:28

Problem 70

Three polarizing sheets are placed together such that the transmission axis of the second sheet is oriented at $25.0^{\circ}$ to the axis of the first, whereas the transmission axis of the third sheet is oriented at $40.0^{\circ}$ (in the same sense) to the axis of the first. What fraction of the intensity of an incident unpolarized beam is transmitted by the combination?

Nicholas Mogoi

Numerade Educator

01:32

Problem 71

In order to rotate the polarization axis of a beam of linearly polarized light by $90.0^{\circ},$ a student places sheets $P_{1}$ and $P_{2}$ with their transmission axes at $45.0^{\circ}$ and $90.0^{\circ},$ respectively, to the beam's axis of polarization. (a) What fraction of the incident light passes through $P_{1}$ and (b) through the combination? (c) Repeat your calculations for part (b) for transmission-axis angles of $30.0^{\circ}$ and $90.0^{\circ},$ respectively.

Mayukh Banik

Numerade Educator

00:24

Problem 72

It is found that when light traveling in water falls on a plastic block, Brewster's angle is $50.0^{\circ} .$ What is the refractive index of the plastic?

Mayukh Banik

Numerade Educator

00:32

Problem 73

At what angle will light reflected from diamond be completely polarized?

Salamat Ali

Numerade Educator

00:29

Problem 74

What is Brewster's angle for light traveling in water that is reflected from crown glass?

Mayukh Banik

Numerade Educator

00:24

Problem 75

A scuba diver sees light reflected from the water's surface. At what angle relative to the water's surface will this light be completely polarized?

Mayukh Banik

Numerade Educator

01:33

Problem 76

From his measurements, Roemer estimated that it took 22 min for light to travel a distance equal to the diameter of Earth's orbit around the Sun. (a) Use this estimate along with the known diameter of Earth's orbit to obtain a rough value of the speed of light. (b) Light actually takes $16.5 \mathrm{min}$ to travel this distance. Use this time to calculate the speed of light.

Mayukh Banik

Numerade Educator

01:29

Problem 77

Comu performed Fizeau's measurement of the speed of light using a wheel of diameter $4.00 \mathrm{cm}$ that contained 180 teeth. The distance from the wheel to the mirror was
$22.9 \mathrm{km} .$ Assuming he measured the speed of light accurately, what was the angular velocity of the wheel?

Mayukh Banik

Numerade Educator

01:24

Problem 78

Suppose you have an unknown clear substance immersed in water, and you wish to identify it by finding its index of refraction. You arrange to have a beam of light enter it at an angle of $45.0^{\circ},$ and you observe the angle of refraction to be $40.3^{\circ} .$ What is the index of refraction of the substance and its likely identity?

Salamat Ali

Numerade Educator

00:37

Problem 79

Shown below is a ray of light going from air through crown glass into water, such as going into a fish tank. Calculate the amount the ray is displaced by the glass $(\Delta x), \quad$ given that the incident angle is $40.0^{\circ}$ and the glass is $1.00 \mathrm{cm}$ thick.

Mayukh Banik

Numerade Educator

00:45

Problem 80

Considering the previous problem, show that $\theta_{3}$ is the same as it would be if the second medium were not present.

Mayukh Banik

Numerade Educator

00:50

Problem 81

At what angle is light inside crown glass completely polarized when reflected from water, as in a fish tank?

Salamat Ali

Numerade Educator

00:47

Problem 82

Light reflected at $55.6^{\circ}$ from a window is completely polarized. What is the window's index of refraction and the likely substance of which it is made?

Salamat Ali

Numerade Educator

01:32

Problem 83

(a) Light reflected at $62.5^{\circ}$ from a gemstone in a ring is completely polarized. Can the gem be a diamond? (b) At what angle would the light be completely polarized if the gem was in water?

Salamat Ali

Numerade Educator

01:24

Problem 84

If $\theta_{b}$ is Brewster's angle for light reflected from the top of an interface between two substances, and $\theta_{\mathrm{b}}^{\prime}$ is Brewster's angle for light reflected from below, prove that $\theta_{\mathrm{b}}+\theta_{\mathrm{b}}^{\prime}=90.0^{\circ}$.

Salamat Ali

Numerade Educator

01:24

Problem 85

Suppose light travels from water to another substance, with an angle of incidence of $10.0^{\circ}$ and an angle of refraction of $14.9^{\circ} .$ (a) What is the index of refraction of the other substance? (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?

Salamat Ali

Numerade Educator

01:39

Problem 86

Unreasonable results Light traveling from water to a gemstone strikes the surface at an angle of $80.0^{\circ}$ and has an angle of refraction of $15.2^{\circ} .$ (a) What is the speed of light in the gemstone? (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?

Salamat Ali

Numerade Educator

01:33

Problem 87

If a polarizing filter reduces the intensity of polarized light to $50.0 \%$ of its original value, by how much are the electric and magnetic fields reduced?

Mayukh Banik

Numerade Educator

01:06

Problem 88

Suppose you put on two pairs of polarizing sunglasses with their axes at an angle of $15.0^{\circ} .$ How much longer will it take the light to deposit a given amount of energy in your eye compared with a single pair of sunglasses? Assume the lenses are clear except for their polarizing characteristics.

Mayukh Banik

Numerade Educator

01:20

Problem 89

(a) On a day when the intensity of sunlight is $1.00 \mathrm{kW} / \mathrm{m}^{2},$ a circular lens $0.200 \mathrm{m}$ in diameter focuses light onto water in a black beaker. Two polarizing sheets of plastic are placed in front of the lens with their axes at an angle of $20.0^{\circ} .$ Assuming the sunlight is unpolarized and the polarizers are $100 \%$ efficient, what is the initial rate of heating of the water in $^{\circ} \mathrm{C} / \mathrm{s},$ assuming it is $80.0 \%$ absorbed? The aluminum beaker has a mass of 30.0 grams and contains 250 grams of water. (b) Do the polarizing filters get hot? Explain.

Mayukh Banik

Numerade Educator

01:04

Problem 90

Light shows staged with lasers use moving mirrors to swing beams and create colorful effects. Show that a light ray reflected from a mirror changes direction by $2 \theta$ when the mirror is rotated by an angle $\theta$.

Salamat Ali

Numerade Educator

01:26

Problem 91

Consider sunlight entering Earth's atmosphere at sunrise and sunset- -hat is, at a $90.0^{\circ}$ incident angle. Taking the boundary between nearly empty space and the atmosphere to be sudden, calculate the angle of refraction for sunlight. This lengthens the time the Sun appears to be above the horizon, both at sunrise and sunset. Now construct a problem in which you determine the angle of refraction for different models of the atmosphere, such as various layers of varying density. Your instructor may wish to guide you on the level of complexity to consider and on how the index of refraction varies with air density.

Mayukh Banik

Numerade Educator

01:21

Problem 92

A light ray entering an optical fiber surrounded by air is first refracted and then reflected as shown below. Show that if the fiber is made from crown glass, any incident ray will be totally internally reflected.

Mayukh Banik

Numerade Educator

00:40

Problem 93

A light ray falls on the left face of a prism (see below)
at the angle of incidence $\theta$ for which the emerging beam has an angle of refraction $\theta$ at the right face. Show that the index of refraction $n$ of the glass prism is given by.
$$n=\frac{\sin \frac{1}{2}(\alpha+\phi)}{\sin \frac{1}{2} \phi}$$
where $\phi$ is the vertex angle of the prism and $\alpha$ is the angle through which the beam has been deviated. If $\alpha=37.0^{\circ}$ and the base angles of the prism are each $50.0^{\circ},$ what is
$n ?$

Mayukh Banik

Numerade Educator

01:31

Problem 94

If the apex angle $\phi$ in the previous problem is $20.0^{\circ}$ and $n=1.50,$ what is the value of $\alpha$ ?

Mayukh Banik

Numerade Educator

01:58

Problem 95

The light incident on polarizing sheet $P_{1}$ is linearly polarized at an angle of $30.0^{\circ}$ with respect to the transmission axis of $\mathrm{P}_{1} .$ Sheet $\mathrm{P}_{2}$ is placed so that its
axis is parallel to the polarization axis of the incident light, that is, also at $30.0^{\circ}$ with respect to $\mathrm{P}_{1}$. (a) What fraction
of the incident light passes through $P_{1} ?$ (b) What fraction
of the incident light is passed by the combination? (c) By rotating $\mathrm{P}_{2},$ a maximum in transmitted intensity is obtained. What is the ratio of this maximum intensity to the intensity of transmitted light when $P_{2}$ is at $30.0^{\circ}$ with respect to $\mathrm{P}_{1} ?$

Mayukh Banik

Numerade Educator

01:09

Problem 96

Prove that if $I$ is the intensity of light transmitted by two polarizing filters with axes at an angle $\theta$ and $I^{\prime}$ is the intensity when the axes are at an angle $90.0^{\circ}-\theta$
then $I+I^{\prime}=I_{0}, \quad$ the original intensity. (Hint: Use the trigonometric identities $\cos 90.0^{\circ}-\theta=\sin \theta \quad$ and $\left.\cos ^{2} \theta+\sin ^{2} \theta=1 .\right)$

Salamat Ali

Numerade Educator