# College Physics 2013

## Educators

FT

### Problem 1

Sound interference Two sources of sound waves are 2.0 m apart and vibrate in phase, producing sinusoidal sound waves of wavelength 1.0 m. (a) Use the wave front representation to explain what happens to the amplitude of sound along a line equidistant from each source and perpendicular to the line connecting the sources. (b) Use a graphical representation (pressure-versus-position graph) to explain what happens along that line. (c) Which representation is more helpful? Explain.

### Problem 2

Green light of wavelength 540 nm is incident on two slits that are separated by 0.50 mm. (a) Make a list of physicalquantities you can determine using this information and determine three of them. (b) What do you need to change to double the distance between the 0th and the first bright spot on the screen?

FT
Francisco T.

### Problem 3

Blue light of wavelength 440 nm is incident on two slits separated by 0.30 mm. Determine (a) the angular deflection to the center of the 3rd order bright band and (b) its spatial separation from the 0th order band when the light is projected on a screen located 3.0 m from the slits. (c) Draw a sketch (not to scale) that schematically represents this situation and label all known distances and angles.

### Problem 4

Red light of wavelength 630 nm passes through two slits and then onto a screen that is 1.2 m from the slits. The center of the 3rd order bright band on the screen is separated from the central maximum by 0.80 cm. What can you determine using this information?

FT
Francisco T.

### Problem 5

Sound from speakers Sound of frequency 680 Hz is synchronized as it leaves two speakers that are separated by 0.80 m on an open field. Draw a sketch of this arrangement and draw a line from between the speakers to a location where the sound is intense and equidistance from the two speakers
(the 0th order maximum). Determine the angular deflection of a line from between the speakers to the 1st order intensity maximum to the side of this 0th order maximum. The speed of sound is 340 m/s.

### Problem 6

Sketch a moving wave front Draw a sketch of two narrow slits separated by 4.0 cm. On the sketch, show the crests of six waves of wavelength 1.0 cm that have left each slit. Draw lines from a point halfway between the slits in the directions of the center of the 0th order and 1st order intensity maxima. Draw a screen 7.0 cm from the slits and use your sketch to estimate the distance between the center of the central maximum on the screen and a 1st order bright spot to the side. Check your results using equations from the text. Were your sketch-based estimated results within 20% of the mathematical results?

FT
Francisco T.

### Problem 7

Neon lamp A neon lamp emits light that looks orange. After passing through a narrow single slit, the light strikes two very narrow slits separated by distance d and located a distance D from the single slit. After passing through the pair of slits, the light strikes a screen a distance L away. (a) Make a sketch of the pattern that you would expect to see on the screen if light behaves like a wave. (b) Below the interference
pattern, sketch the pattern that you would expect to see if light behaves like a stream of very light particles. Use correct dimensions in both cases.

### Problem 8

Characteristics of laser light when in glass A laser light in air has a wavelength of 670 nm. What is the frequency of the light? What is the frequency of this light when it travels in glass? In water? What is the wavelength of light in these media? (Use Table 21.7 if needed.)

FT
Francisco T.

### Problem 9

Prism converts white light Use the wave model of light to explain why white light striking a side of a triangular prism emerges as a spectrum.

### Problem 10

Representing how grating works Use the representation (wave fronts or rays) that you think is best to explain why monochromatic light forms a pattern of narrow bright and wide dark fringes on a wall when it passes through a grating as opposed to a pattern of wide bright fringes and narrow dark regions produced by a double slit.

FT
Francisco T.

### Problem 11

Light of wavelength 520 nm passes through a grating with 4000 lines/cm and falls on a screen located 1.6 m from the grating. (a) Draw a picture (not to scale) that schematically represents the process and label all known distances and angles. (b) Determine the angular deflection of the second bright band. (c) Determine the separation of the 2nd order bright spot from the central maximum.

### Problem 12

Hydrogen light grating deflection Light of wavelength 656 nm and 410 nm emitted from a hot gas of hydrogen atoms strikes a grating with 5300 lines per centimeter. Determine the angular deflection of both wavelengths in the 1st and 2nd orders.

FT
Francisco T.

### Problem 13

Purchase a grating How many lines per centimeter should a grating have to cause a $38^{\circ}$ deflection of the 2 nd order bright band of 680 -nm red light?

### Problem 14

Only half a grating The left side of the grating from the previous problem breaks off. Half of the slits are missing. How will it affect the location of the 2nd order bright band?

FT
Francisco T.

### Problem 15

Design Design a quick way to estimate which one of two gratings has more lines per centimeter.

### Problem 16

Laser light on grating 1 The 630-nm light from a helium neon laser irradiates a grating. The light then falls on a screen where the first bright spot is separated from the central maximum by 0.51 m. Light of another wavelength of light produces its first bright spot 0.43 m from its central maximum. Determine the second wavelength.

FT
Francisco T.

### Problem 17

Laser light on grating 2 Light of wavelength 630 nm passes through a grating and then onto a screen located several meters from the grating. The 1st order bright band is located 0.28 m from the central maximum. Light from a second source produces a band 0.20 m from the central maximum. Determine the wavelength of the second source. Show your calculations. [Hint: If the angular deflection is small, $\tan \theta=\sin \theta . ]$

### Problem 18

Representing thin-film interference (a) Draw a ray diagram for a laser beam incident from air on a thin film that has air on the other side. Make sure to take into account the processes occurring on each surface of the film. (b) Discuss in words what happens to the wave phase at each boundary. (c) Under what conditions will a person observe no reflected light?

FT
Francisco T.

### Problem 19

$*$ Oil film on water A thin film of vegetable oil $(n=1.45)$ is floating on top of water $(n=1.33) .$ (a) Describe in words the processes occurring to a laser beam at the top and bottom surfaces of the oil. (b) Is it possible to have a film of water on top of the oil surface? Explain your answer.

### Problem 20

Soap bubble 1 You look at a soap bubble film perpendicular to its surface. Describe the changes in colors of the film that you observe as the film thins and eventually breaks. Support your explanation with a ray diagram and a disturbance-versus-position graph.

FT
Francisco T.

### Problem 21

$*$ Soap bubble 2 A soap bubble of refractive index 1.40 appears blue-green when viewed perpendicular to its surface (blue-green appears when red light is missing from the continuous spectrum, where $\lambda_{\text { red }}$ is about 670 $\mathrm{nm}$ in a vacuum). Does the light change phase when reflected from (a) the outside surface of the bubble and (b) the inside surface? (c) Determine the wavelength of red light when passing through the bubble. (d) Determine the thickness of the thinnest bubble for which the 670-nm red light reflected from the outside surface of the bubble interferes destructively with light reflected from the inside surface.

### Problem 22

Thin-film coated lens A lens coated with a thin layer of material having a refractive index 1.25 reflects the least amount of light at wavelength 590 nm. Determine the minimum thickness of the coating.

FT
Francisco T.

### Problem 23

Thin-film coated glass plate A film of transparent material 120 nm thick and having refractive index 1.25 is placed on a glass sheet having refractive index 1.50. Determine (a) the longest wavelength of light that interferes destructively when reflected from the film and (b) the longest wavelength that interferes constructively.

### Problem 24

Two flat glass surfaces are separated by a 150-nm gap of air. (a) Explain why 600-nm-wavelength light illuminating the air gap is reflected brightly. (b) What wavelength of radiation is not reflected from the air gap?

FT
Francisco T.

### Problem 25

Explain diffraction Draw a ray diagram and show path length differences to explain how wavelets originating in different parts of a slit produce the third dark fringe on a distant screen.

### Problem 26

How did we derive it? Explain how we derived the equation for the first dark fringe for single-slit diffraction. Draw a ray diagram or a disturbance-versus-position graph to help in your explanation. Show the path length difference and the phase differences.

FT
Francisco T.

### Problem 27

Explain a white light diffraction pattern White light passing through a single slit produces a white bright band at the center of the pattern on a screen and colored bands at the sides. Explain.

### Problem 28

Light of wavelength 630 nm is incident on a long, narrow slit. Determine the angular deflection of the first diffraction minimum if the slit width is (a) 0.020 mm, (b) 0.20 mm, and (c) 2.0 mm.

FT
Francisco T.

### Problem 29

Light of wavelength of 120 nm is incident on a long, narrow slit of width 0.050 mm. Determine the angular deflection of the 5th order diffraction minimum.

### Problem 30

Sound diffraction through doorway Sound of frequency 440 $\mathrm{Hz}$ passes through a doorway opening that is 1.2 $\mathrm{m}$ wide. Determine the angular deflection to the first and second diffraction minima $\left(v_{\text { sound }}=340 \mathrm{m} / \mathrm{s}\right)$

FT
Francisco T.

### Problem 31

Light of wavelength 624 nm passes through a single slit and then strikes a screen that is 1.2 m from the slit. The thin dark band is 0.60 cm from the central bright band. Determine the slit width.

### Problem 32

Explain resolution Explain the term “resolution limit.” Illustrate your explanation with pictures and ray diagrams, and explain what characteristics of an optical device and the light passing through it affect the resolution limit.

FT
Francisco T.

### Problem 33

Resolution of telescope A large telescope has a 3.00-m-radius mirror. What is the resolution limit of the telescope? What assumptions did you make?

### Problem 34

Laser light of wavelength 630 nm passes through a tiny hole. The angular deflection of the first dark band is $26^{\circ} .$ What can you learn about the hole using this information?

FT
Francisco T.

### Problem 35

Size of small bead Infrared radiation of wavelength 1020 $\mathrm{nm}$ passes a dark, round glass bead and produces a circular diffraction pattern 0.80 $\mathrm{m}$ beyond it. The diameter of the
first bright circular ring is 6.4 $\mathrm{cm} .$ What can you learn about the bead using this information?

### Problem 36

Resolution of telescope How will the resolution limit of a telescope change if you take pictures of stars using a blue filter as opposed to using a red filter? Explain.

FT
Francisco T.

### Problem 37

Detecting visual binary stars Struve 2725 is a double-star system with a visual separation of 5.7 arcseconds in the constellation Delphinus. Determine the minimum diameter of the objective lens of a telescope that will allow you to resolve 400-nm violet light from the two stars.

### Problem 38

Hubble Telescope resolving power The objective mirror of the Hubble Telescope is 2.4 $\mathrm{m}$ in diameter. Could it resolve the binary stars Lambda Cas in the constellation Cassiopeia? The stars have an angular separation of 0.5 arcseconds.

FT
Francisco T.

### Problem 39

Draw a graphical representation of Rayleigh’s criterion. Explain how this criterion relates to the concept of the resolution limit.

### Problem 40

Ability of a bat to detect small objects Bats emit ultrasound in order to detect prey. Ultrasound has a much smaller wavelength than sound, which improves the resolution of small objects. What is the diameter of the smallest object that forms a diffraction pattern when irradiated by the $8.0 \times 10^{4}$ -Hz ultrasound from a bat? The first diffraction minimum from the smallest object is $90^{\circ} .$

FT
Francisco T.

### Problem 41

Red light from a helium-neon gas laser has a wave-length of 630 nm and passes through two slits. (a) Draw a ray diagram to explain why you see a pattern of bright and dark bands on the screen. Show the path length difference. (b) Determine the angular deflection of the light to the first three bright bands when incident on narrow slits separated by 0.40 mm. (c) Determine the spatial separation of the centers of 0th and 2nd order bright bands when projected on a screen located 5.0 m from the slits. (d) List all of the assumptions that you made in your calculations.

### Problem 42

Red light of wavelength 630 nm is incident on a pair of slits. The interference pattern is projected on a wall 6.0 m from the slits. The fourth bright band is separated from the central maximum by 2.8 cm. (a) Draw a ray diagram to represent the situation; show the path length difference. (b) What can you learn about the slit pair using this information? (c) What can you learn about the pattern on the screen using
this information?

FT
Francisco T.

### Problem 43

Monochromatic light passes through a pair of slits separated by 0.025 mm. On a screen 2.0 m from the slits, the 3rd order bright fringe is separated from the central maximum by 15 cm. (a) Draw a ray diagram to represent the situation. Show the path length difference. (b) What can you learn about the light source using this information?

### Problem 44

Ratio reasoning Two different wavelengths of light shine on the same grating. The 3rd order line of wavelength A $\left(\lambda_{\mathrm{A}}\right)$ has the same angular deflection as the 2 nd order line of wavelength $\mathrm{B}\left(\lambda_{\mathrm{B}}\right) .$ Determine the ratio $\left(\lambda_{\mathrm{A}} / \lambda_{\mathrm{B}}\right) .$ Be sure to show the reasoning leading to your solution.

FT
Francisco T.

### Problem 45

Design an experiment to use a grating to determine the wavelengths of light of different colors. Draw a
picture of the apparatus. List the quantities that you will measure. Describe the mathematical procedure that you will use to calculate the wavelengths.

### Problem 46

Fence acts as a grating for sound A fence consists of alternating slats and openings, the openings being separated from each other by 0.40 m. Parallel wave fronts of a single-frequency sound wave irradiate the fence from one side. A person 20 m from the fence walks parallel to it. She hears intense sound directly in front of the fence and in another region 15 m farther along a line parallel to the fence. Determine everything you can about the sound used in this problem (the speed of sound is 340 m/s).

FT
Francisco T.

### Problem 47

Morpho butterfly reflection grating wings A reflection grating reflects light from adjacent lines in the grating instead of allowing the light to pass through slits, as in a transmission grating. If we assume perpendicular incidence, then we can determine the angular deflection of bright bands the same way we did for a transmission grating. White light is incident on the wing of a Morpho butterfly (whose wings act as reflection gratings). Red light of wavelength 660 nm is vMorpho butterfly reflection grating wings A reflection grating reflects light from adjacent lines in the grating instead of allowing the light to pass through slits, as in a transmission grating. If we assume perpendicular incidence, then we can determine the angular deflection of bright bands the same way we did for a transmission grating. White light is incident on the wing of a Morpho butterfly (whose wings act as reflection gratings). Red light of wavelength 660 nm is Morpho butterfly reflection grating wings A reflection grating reflects light from adjacent lines in the grating instead of allowing the light to pass through slits, as in a transmission grating. If we assume perpendicular incidence, then we can determine the angular deflection of bright bands the same way we did for a transmission grating. White light is incident on the wing of a Morpho butterfly (whose wings act as reflection gratings). Red light of wavelength 660 nm is deflected in the 1 st order at an angle of $1.2^{\circ} .$ (a) Determine the angular deflection in the 1 st order of blue light $(460 \mathrm{nm})$ . (b) Determine the angular deflection in the 3 rd order of yellow light $(560 \mathrm{nm})$

### Problem 48

Ratio reasoning Laser monochromatic light is used to illuminate two different gratings. The angular deflection of the 2nd order band of light leaving grating A equals the angular deflection of the 3rd order band from grating B. Determine the ratio of the number of lines per centimeter for grating A and for grating B.

FT
Francisco T.

### Problem 49

Soap bubble interference Light of 690-nm wavelength interferes constructively when reflected from a soap bubble having refractive index 1.33. Determine two possible thicknesses of the soap bubble.

### Problem 50

Oil film on water A film of oil with refractive index 1.50 is spread on water whose refractive index is 1.33. Determine the smallest thickness of the film for which reflected green light of wavelength 520 nm interferes destructively.

FT
Francisco T.

### Problem 51

Babinet’s principle Babinet’s principle states that the diffraction pattern of complementary objects is the same. For example, a rectangular slit in a screen produces the same diffraction pattern as a rectangular screen the same size as the slit; a hair should produce the same diffraction pattern as a slit of the same
width. Determine the width of a hair that, when irradiated with laser light of wavelength 630 nm, produces a diffraction pattern on a screen with the first minimum 2.5 cm on the side of the central maximum. The screen is 2.0 m from the hair.

### Problem 52

Diffraction from sound speaker The opening of a stereo speaker is shaped like a slit. Determine the maximum width such that the first diffraction minimum of sound is at least $45^{\circ}$ on each side of the direction in which the speaker points. Perform the calculations for sound waves of frequency (a) 200 $\mathrm{Hz}$ , (b) 1000 $\mathrm{Hz}$ , and (c) $10,000$ Hz. The speed of sound is 340 $\mathrm{m} / \mathrm{s}$ .

FT
Francisco T.

### Problem 53

The angular deflection of the 1 st order bright band of light passing through double slits separated by 0.20 $\mathrm{mm}$ is $0.15^{\circ} .$ Determine the angular deflection of the 3 rd order diffraction
minimum when the same light passes through a single slit of width 0.30 $\mathrm{mm}$ .

### Problem 54

Diffraction of sound from the mouth (a) Estimate the diameter of your mouth when open wide. (b) Determine the angular deflection of $200-\mathrm{Hz}$ sound and of $15,000-\mathrm{Hz}$ sound
as it leaves your mouth. If, during your calculations, you find that $\sin \theta>1$ , explain the meaning of this result. The speed of sound is 340 $\mathrm{m} / \mathrm{s}$ .

FT
Francisco T.

### Problem 55

Determine body cell size Light of 630 $\mathrm{nm}$ wavelength from a helium-neon laser passes two different-size body cells. The angular deflection of the light as it passes the cells is (a) 0.060 radians and (b) 0.085 radians. Determine the size of each cell.

### Problem 56

A sound of frequency 1000 Hz passes a basketball. Estimate the angular deflection from the basketball to the first ring around the central maximum in the diffraction pattern. The speed of sound is 340 m>s.

FT
Francisco T.

### Problem 57

Monochromatic light passes through two slits and then strikes a screen. The distance separating the central maximum and the first bright fringe at the side is 2.0 cm. Determine the fringe separation when the following quantities change simultaneously: the slit separation is doubled, the wavelength of light is increased 30%, and the screen distance is halved.

### Problem 58

Sound from speakers Two stereo speakers separated by a distance of 2.0 m play the same musical note at frequency 1000 Hz. A listener starts from position 0 (Figure P23.58) and walks along a line parallel to the speakers. (a) Can the listener easily hear the sound at position 0? Explain. (b) Calculate the distance from position 0 to positions 1 and 2 where intense sound is also heard. The speed of sound is 340 m/s.

FT
Francisco T.

### Problem 59

Astronomer's spectrograph An astronomer has a grating spectrograph with 5000 lines $/ \mathrm{cm} .$ A film 0.500 $\mathrm{m}$ from the grating records bands of light passing through the grating. (a) Determine the wavelength and frequency of the $\mathrm{H}_{\alpha}$ line of hydrogen gas in a laboratory discharge tube that produces a lst order band separated on the film by 17.4 $\mathrm{cm}$ from the central maximum. (b) Determine the wavelength and frequency of the $\mathrm{H}_{\alpha}$ line coming from a galaxy in the cluster Hydra A. The 1 st order band of the $\mathrm{H}_{\alpha}$ line of this light is 18.4 $\mathrm{cm}$ from the central maximum. (c) Suggest a possible reason for the differences in the frequency of the $\mathrm{H}_{\alpha}$ line from a lab source and the $\mathrm{H}_{\alpha}$ line from the galaxy.

### Problem 60

Diffraction of water waves entering a harbor The wave-length of water waves entering a harbor is 14 $\mathrm{m} .$ The angular deflection of the 1 st order diffraction minimum of the waves in the water beyond the harbor is $38^{\circ} .$ Determine the width of the opening into the harbor.

FT
Francisco T.

### Problem 61

Effect of shrinking Earth Assume that Earth, its structures, and its inhabitants are all decreased in size by the same factor. Estimate the decrease required in order that the 1 st order diffraction dark band of 500 nm light entering a typical room window is at $90^{\circ}$ (the central bright band would light
most of the room.). Explain all aspects of your calculations.

### Problem 62

Variable thickness wedge A wedge of glass of refractive index 1.64 has a silver coating on the bottom, as shown in Figure P23.62. Determine the smallest distance x to a position where 500@nm light reflected from the top surface of the glass interferes constructively with light reflected from the silver coating on the bottom. The light changes phase when reflected at the silver coating.

FT
Francisco T.

### Problem 63

Resolving car headlights Estimate the farthest away a car can be at night so that your eyes can resolve the two head-lights. Indicate any assumptions you made.

### Problem 64

Looking at Moon rocks You have a home telescope with a 3.0@cm objective lens. Determine the closest distance between two large boulders on the Moon that you can distinguish as separate objects. Indicate any assumptions you made.

FT
Francisco T.

### Problem 65

Diffraction-limited resolving power of the eye You look at closely spaced lines on a wall 5.0 m from your
eyes. Estimate the closest the lines can be to each other and still be resolved by your eyes as separate lines. Indicate any assumptions you made in making your estimate.

### Problem 66

Resolving sunspots You are looking at sunspots. They usually appear in pairs on the surface of the Sun. The Sun is about $1.5 \times 10^{11} \mathrm{m}$ from Earth. How close can two sunspots be so
you can distinguish them when they are observed though an amateur telescope whose aperture (objective lens) is about 20 $\mathrm{cm} ?$ Describe all of the assumptions that you made.

FT
Francisco T.

### Problem 67

The Moon’s Mare Imbrium The outermost ring of mountains surrounding the Mare Imbrium on the Moon has a diameter of 1300 km. What diameter objective lens telescope would allow an astronomer to see the ring of mountains as a distinct feature of the Moon’s landscape? What assumptions did you
make? The average center-to-center distance from the Earth to the Moon is 384,403 km, which is about 30 times the diameter of the Earth. The Moon has a diameter of 3474 km.

### Problem 68

Can you see atoms with a light-based microscope? Explain how you can use your knowledge of the wave model of light to explain why you cannot use an optical microscope to see atoms.

FT
Francisco T.

### Problem 69

Detecting insects by diffraction of sound A biologist builds a device to detect and measure the size of insects. The device emits sound waves. If an insect passes through the beam of sound waves, it produces a diffraction pattern on an array of sound detectors behind the insect. What is the
lowest-frequency sound that can be used to detect a fly that is about 3 mm in diameter? The speed of sound is 340 m/s.

### Problem 70

Which answer below is closest to the height of the letters that a person with 20/80 vision can distinguish when 20 ft from the wall chart?
(a) 2.2 mm (b) 4.4 mm (c) 8.8 mm
(d) 18 mm (e) 34 mm

FT
Francisco T.

### Problem 71

Suppose that a person with 20/20 vision stands 30 ft from a Snellen eye chart. Which answer below is closest to the minimum height of the letters the person can distinguish?

(a) 4.4 mm (b) 6.6 mm (c) 8.8 mm
(d) 13 mm (e) 18 mm

### Problem 72

What is the visual acuity of a person with 20/20 vision mainly limited by?
(a) The Rayleigh criterion
(b) Chromatic aberration
(c) Focal length of the eye lens
(d) Diameter of the eye’s pupil
(e) The density of cones and rods
(f) A combination of these factors

FT
Francisco T.

### Problem 73

A hawk’s vision is said to be 20/5. If so, the hawk can distinguish 8.8-mm-tall letters from about what distance?

(a) 5 ft (b) 10 ft (c) 40 ft
(d) 80 ft (e) 120 ft

### Problem 74

If the vision of a hawk is actually 20$/ 5$ , then the angular resolution of the hawk is closest to what angle? Assume that it can distinguish objects about 8.8 $\mathrm{mm}$ from a distance of 60 $\mathrm{m}$ . (Compare your answer to this question and the previous question to decide if the Rayleigh criterion is the limiting factor in a hawk's resolving ability.)
$\begin{array}{ll}{\text { (a) } 0.2 \times 10^{-4} \mathrm{rad}} & {\text { (b) } 0.5 \times 10^{-4} \mathrm{rad}} \\ {\text { (c) } 1 \times 10^{-4} \mathrm{rad}} & {\text { (d) } 2 \times 10^{-4} \mathrm{rad}}\end{array}$

FT
Francisco T.

### Problem 75

The hawk shown in Figure $P 23.74$ is only about 50 $\mathrm{cm}$ tall and has smaller eyes and pupils than the human eye. Estimate the Rayleigh criterion for this hawk.
$\begin{array}{ll}{\text { (a) } 1 \times 10^{-4} \mathrm{rad}} & {\text { (b) } 3 \times 10^{-4} \mathrm{rad}} \\ {\text { (c) } 10 \times 10^{-4} \mathrm{rad}} & {\text { (d) } 20 \times 10^{-4} \mathrm{rad}} \\ {\text { (e) } 40 \times 10^{-4} \mathrm{rad}}\end{array}$

### Problem 76

Which of the following are benefits of thin-film coatings on windows?
(a) They keep ultraviolet light out of the house in summer and winter.
(b) They keep infrared radiation out of the house in the summer.
(c) They keep infrared radiation in the house in the winter.
(d) b and c
(e) a, b, and c

FT
Francisco T.

### Problem 77

A 1.25 refractive index thin film on a 1.50 refractive index glass window is made to reflect infrared radiation of wave-length 1000 nm. What is the net reflective phase change of infrared radiation reflected off the front surface of the thin film relative to the radiation reflected off the back surface of the
film and returning to the front?
(a) Zero (b) 1/4 wavelength
(c) 1/2 wavelength (d) None of these

### Problem 78

A 1.25 refractive index thin film on a 1.50 refractive index glass window is made to reflect infrared radiation of wave-length 1000 nm. Which wavelength below is closest to the wavelength of the infrared radiation while in the thin film?
(a) 670 nm (b) 800 nm (c) 1000 nm
(d) 1250 nm (e) 1500 nm

FT
Francisco T.

### Problem 79

A 1.25 refractive index thin film on a 1.50 refractive index glass window is made to reflect infrared radiation of wave-length 1000 nm. Which answer is closest to the desired thickness of the thin film?

(a) 200 nm (b) 250 nm (c) 400 nm
(d) 500 nm (e) 1000 nm