University Physics with Modern Physics

Wolfgang Bauer, Gary D. Westfall

Chapter 34

Wave Optics - all with Video Answers

Educators

Chapter Questions

Problem 1

Suppose the distance between the slits in a double-slit experiment is $2.00 \cdot 10^{-5} \mathrm{~m}$. A beam of light with a wavelength of $750 \mathrm{nm}$ is shone on the slits. What is the angular separation between the central maximum and an adjacent maximum?
a) $5.00 \cdot 10^{-2} \mathrm{rad}$
c) $3.75 \cdot 10^{-2} \mathrm{rad}$
b) $4.50 \cdot 10^{-2} \mathrm{rad}$
d) $2.50 \cdot 10^{-2} \mathrm{rad}$

Narayan Hari

Narayan Hari

Numerade Educator

Problem 2

When two light waves, both with wavelength $\lambda$ and amplitude $A$, interfere constructively, they produce a light wave of the same wavelength but with amplitude $2 A$. What is the intensity of this light wave?
a) same intensity as the original waves
b) double the intensity of the original waves
c) quadruple the intensity of the original waves
d) Not enough information is given.

Narayan Hari

Numerade Educator

Problem 3

A laser beam with wavelength $633 \mathrm{nm}$ is split into two beams by a beam splitter. One beam goes to mirror 1 , a distance $L$ from the beam splitter, and returns to the beam splitter, while the other beam goes to mirror $2,$ a distance $L+\Delta x$ from the beam splitter, and returns to the beam splitter. The beams then recombine and travel to a detector together. If $L=1.00000 \mathrm{~m}$ and $\Delta x=1.00 \mathrm{~mm},$ which best describes the kind of interference observed at the detector? (Hint: To double-check your answer, you may need to use a formula that was originally intended for combining two beams in a different geometry.)
a) purely constructive
b) purely destructive
c) mostly constructive
d) mostly destructive
e) neither constructive nor destructive

Narayan Hari

Numerade Educator

Problem 4

Which type of the light incident on a grating with 1000 rulings with a spacing of $2.00 \mu \mathrm{m}$ would produce the largest number of maxima on a screen $5.00 \mathrm{~m}$ away? $?$
a) blue light of wavelength $450 \mathrm{nm}$
b) green light of wavelength $550 \mathrm{nm}$
c) yellow light of wavelength $575 \mathrm{nm}$
d) red light of wavelength $625 \mathrm{nm}$
e) need more information

Narayan Hari

Numerade Educator

Problem 5

If the wavelength of light illuminating a double slit is halved, the fringe spacing is
a) halved.
c) not changed.
b) doubled.
d) changed by a factor of $1 / \sqrt{2}$.

Narayan Hari

Numerade Educator

Problem 6

A red laser pointer shines light with a wavelength of $635 \mathrm{nm}$ on a diffraction grating with 300 slits $/ \mathrm{mm}$. A screen is placed a distance of $2.0 \mathrm{~m}$ behind the diffraction grating to observe the diffraction pattern. How far away from the central maximum will the next bright spot be on the screen?
a) $39 \mathrm{~cm}$
c) $94 \mathrm{~cm}$
e) $9.5 \mathrm{~m}$
b) $76 \mathrm{~cm}$
d) $4.2 \mathrm{~m}$

Ajay Singhal

Numerade Educator

Problem 7

Newton's rings are interference patterns caused by the reflection of light between two glass surfaces. What color is the center of Newton's rings produced with white light?
a) white
c) red
b) black
d) violet

Ajay Singhal

Numerade Educator

Problem 8

In Young's double-slit experiment, both slits were illuminated by a laser beam and the interference pattern was observed on a screen. If the viewing screen is moved farther from the slits, what happens to the interference pattern?
a) The pattern gets brighter.
b) The pattern gets brighter, and the maxima are closer together.
c) The pattern gets less bright, and the maxima are farther apart.
d) There is no change in the pattern.
e) The pattern becomes unfocused.
f) The pattern disappears.

Ajay Singhal

Numerade Educator

Problem 9

Light of wavelength $=560.0 \mathrm{nm}$ enters a block of clear plastic from air at an incident angle of $\theta_{\mathrm{i}}=36.1^{\circ}$ with respect to the normal. The angle of refraction is $\theta_{\mathrm{r}}=21.7^{\circ} .$ What is the speed of the light inside the plastic?
a) $1.16 \cdot 10^{8} \mathrm{~m} / \mathrm{s}$
c) $1.67 \cdot 10^{8} \mathrm{~m} / \mathrm{s}$
e) $3.00 \cdot 10^{8} \mathrm{~m} / \mathrm{s}$
b) $1.31 \cdot 10^{8} \mathrm{~m} / \mathrm{s}$
d) $1.88 \cdot 10^{8} \mathrm{~m} / \mathrm{s}$

Narayan Hari

Numerade Educator

Problem 10

Huygens's Principle says that each point of a wave front in a slit is a point source of light emitting a spherical wavelet. A Huygens construction applies
a) to any point anywhere in the path of the wave front.
b) to any point in the path of the wave front where matter is present.
c) only in slits.

Ajay Singhal

Numerade Educator

Problem 11

If Huygens's Principle holds everywhere, why does a laser beam not spread out?
a) All the light waves that spread in the perpendicular direction from the beam interfere destructively.
b) It does spread out, but the spread is so small that we don't notice it.
c) Huygens's Principle isn't true in general; it only applies to slits, edges, and other obstacles.
d) Lasers employ additional special beams to keep the main beam from spreading.

Ajay Singhal

Numerade Educator

Problem 12

A pair of thin slits is separated by a distance $d=1.40 \mathrm{~mm}$ and is illuminated with light of wavelength $460.0 \mathrm{nm} .$ What is the separation between adjacent interference maxima on a screen a distance $L=2.90 \mathrm{~m}$ away?
a) $0.00332 \mathrm{~mm}$
b) $0.556 \mathrm{~mm}$
c) $0.953 \mathrm{~mm}$
d) $1.45 \mathrm{~mm}$
e) $3.23 \mathrm{~mm}$

Narayan Hari

Numerade Educator

Problem 13

What happens to a double-slit interference pattern if
a) the wavelength is increased?
b) the separation between the slits is increased?
c) the experimental apparatus is placed in water?

Ajay Singhal

Numerade Educator

Problem 14

Estimate the frequency of an ultrasonic (sound) wave for which diffraction effects would be as small as they are for visible light.

Ajay Singhal

Numerade Educator

Problem 15

Why are radio telescopes so much larger than optical telescopes? Does an X-ray telescope also have to be larger than an optical telescope?

Ajay Singhal

Numerade Educator

Problem 16

Can light pass through a single slit narrower than its wavelength? If not, why not? If so, describe the distribution of the light beyond the slit.

Ajay Singhal

Numerade Educator

Problem 17

One type of hologram consists of bright and dark fringes produced on photographic film by interfering laser beams. If the hologram is illuminated with white light, the image will be reproduced multiple times, in different pure colors at different sizes.
a) Explain why.
b) Which colors correspond to the largest and smallest images, and why?

Ajay Singhal

Numerade Educator

Problem 18

A double slit is positioned in front of an incandescent light bulb. Will an interference pattern be produced?

Ajay Singhal

Numerade Educator

Problem 19

Many astronomical observatories, especially radio observatories, are coupling several telescopes together. What are the advantages of this?

Ajay Singhal

Numerade Educator

Problem 20

In a single-slit diffraction pattern, there is a bright central maximum surrounded by successively dimmer higher-order maxima. Farther away from the central maximum, eventually no more maxima are observed. Is this because the remaining maxima are too dim? Or is there an upper limit to the number of maxima that can be observed, no matter how good the observer's eyes, for a given slit and light source?

Ajay Singhal

Numerade Educator

Problem 21

Which close pair of stars will be more easily resolvable with a telescope: two red stars or two blue ones? Assume the binary star systems are the same distance from Earth and are separated by the same angle.

Ajay Singhal

Numerade Educator

Problem 22

A red laser pointer shines on a diffraction grating, producing a diffraction pattern on a screen behind the grating. If the red laser pointer is replaced with a green laser pointer, will the green bright spots on the screen be closer together or farther apart than the red bright spots were?

Ajay Singhal

Numerade Educator

Problem 23

A helium-neon (He-Ne) laser has a wavelength of $632.8 \mathrm{nm}$.
a) What is the wavelength of this light as it passes through Lucite with index of refraction $n=1.500 ?$
b) What is the speed of the light in the Lucite?

Narayan Hari

Numerade Educator

Problem 24

It is common knowledge that the visible light spectrum extends approximately from $400 \mathrm{nm}$ to $700 \mathrm{nm}$. Roughly, $400 \mathrm{nm}$ to $500 \mathrm{nm}$ corresponds to blue light, $500 \mathrm{nm}$ to $550 \mathrm{nm}$ corresponds to green, $550 \mathrm{nm}$ to $600 \mathrm{nm}$ to yellow-orange, and above $600 \mathrm{nm}$ to red. In an experiment, red light with a wavelength of $632.8 \mathrm{nm}$ from a He-Ne laser is refracted into a fish tank filled with water (with index of refraction 1.333 ). What is the wavelength of the laser light in water, and what color will it have in water?

Narayan Hari

Numerade Educator

Problem 25

What minimum path length difference is needed to cause a phase shift of $\pi / 4$ in light of wavelength $700 . \mathrm{nm} ?$

Narayan Hari

Numerade Educator

Problem 26

Coherent, monochromatic light of wavelength $450.0 \mathrm{nm}$ is emitted from two locations and detected at another location. The path length difference between the two routes taken by the light is $20.25 \mathrm{~cm} .$ Will the two light waves interfere destructively or constructively at the detection point?

Narayan Hari

Numerade Educator

Problem 27

A Young's double-slit experiment is performed with monochromatic green light $(\lambda=540 \mathrm{nm})$. The separation between the slits is $0.100 \mathrm{~mm},$ and the interference pattern on a screen has the first side maximum $5.40 \mathrm{~mm}$ from the center of the pattern. How far away from the slits is the screen?

Narayan Hari

Numerade Educator

Problem 28

For a double-slit experiment, two 1.50 -mm-wide slits are separated by a distance of $1.00 \mathrm{~mm} .$ The slits are illuminated by laser light with wavelength $633 \mathrm{nm}$. If a screen is placed $5.00 \mathrm{~m}$ away from the slits, determine the separation of the bright fringes on the screen.

Narayan Hari

Numerade Educator

Problem 29

Coherent monochromatic light with wavelength $\lambda=514 \mathrm{nm}$ is incident on two thin slits that are separated by a distance $d=0.500 \mathrm{~mm}$ The intensity of the radiation at a screen $2.50 \mathrm{~m}$ away is $180.0 \mathrm{~W} / \mathrm{cm}^{2}$. Determine the position $v_{1}$ at which the intensity at the central peak (at $y=0$ ) drops to $I_{0} / 3$ (where $I_{0}$ is the intensity at $\theta=0^{\circ}$ ).

Ajay Singhal

Numerade Educator

Problem 30

In a double-slit experiment, He-Ne laser light of wavelength $633 \mathrm{nm}$ produced an interference pattern on a screen placed some distance from the slits. When one of the slits was covered with a thin glass slide of thickness $12.0 \mu \mathrm{m},$ the central bright fringe shifted to the point occupied earlier by the 10 th dark fringe (see the figure). What is the index of refraction of the glass slide?
(a) Without the glass slide
(b) With glass slide

Ajay Singhal

Numerade Educator

Problem 31

Suppose the thickness of a thin soap film $(n=1.32)$ surrounded by air is nonuniform and gradually tapers. Monochromatic light of wavelength $550 \mathrm{nm}$ illuminates the film. At the thinnest end, a dark fringe is observed. How thick is the film at the two dark fringes closest to that fringe?

Narayan Hari

Numerade Educator

Problem 32

White light $(400 . \mathrm{nm}<\lambda<700 . \mathrm{nm})$ shines onto a puddle of water $(n=1.33)$. There is a thin $(100.0 \mathrm{nm}$ thick $)$ layer of oil $(n=1.47)$ on top of the water. What wavelengths of light would you see reflected?

Narayan Hari

Numerade Educator

Problem 33

Some mirrors for infrared lasers are constructed with alternating layers of hafnia and silica. Suppose you want to produce constructive interference from a thin film of hafnia $(n=1.90)$ on $\mathrm{BK}-7$ glass $(n=1.51)$ using infrared radiation of wavelength $1.06 \mu \mathrm{m} .$ What is the smallest film thickness that would be appropriate, assuming that the laser beam is oriented at right angles to the film?

Narayan Hari

Numerade Educator

Problem 34

Sometimes thin films are used as filters to prevent certain colors from entering a lens. Suppose an infrared filter is to be designed to prevent 800.0 -nm light from entering a lens. Find the minimum thickness for a film of $\mathrm{MgF}_{2}(n=1.38)$ that will prevent this light from entering the lens.

Narayan Hari

Numerade Educator

Problem 35

White light shines on a sheet of mica that has a uniform thickness of $1.30 \mu \mathrm{m} .$ When the reflected light is viewed using a spectrometer, it is noted that light with wavelengths of $433.3 \mathrm{nm}, 487.5 \mathrm{nm}, 557.1 \mathrm{nm}, 650.0 \mathrm{nm}$, and $780.0 \mathrm{nm}$ is not present in the reflected light. What is the index of refraction of the mica?

Narayan Hari

Numerade Educator

Problem 36

A single beam of coherent light $\left(\lambda=633 \cdot 10^{-9} \mathrm{~m}\right)$ is incident on two glass slides, which are touching at one end and are separated by a 0.0200 -mm-thick sheet of paper on the other end, as shown in the figure. Beam 1 reflects off the bottom surface of the top slide, and beam 2 reflects off the top surface of the bottom slide. Assume that all the beams are perfectly vertical and are perpendicular to both slides, that is, the slides are nearly parallel (the angle is exaggerated in the figure); the beams are shown at angles in the figure so that they are easier to identify. Beams 1 and 2 recombine at the location of the eye. The slides are $8.00 \mathrm{~cm}$ long. Starting from the left end $(x=0)$, at what positions, $x_{\text {bright }}$, do bright bands appear to the observer above the slides? How many bright bands are observed?

Keshav Singh

Numerade Educator

Problem 37

A common interference setup for seeing Newton's rings consists of a plano-convex lens placed on a plane mirror and illuminated from above at normal incidence with monochromatic light. In an experiment using a plano-convex lens with focal length $f=80.00 \mathrm{~cm}$ and index of refraction $n_{1}=1.500$, the radius of the third bright circle is found to be $0.8487 \mathrm{~mm} .$ Determine the wavelength of the monochromatic light

Narayan Hari

Numerade Educator

Problem 38

A Michelson interferometer is used in a class of commercially available optical instruments called wavelength meters. In a wavelength meter, the interferometer is illuminated simultaneously with parallel beams from a reference laser of known wavelength and an unknown laser. The movable mirror of the interferometer is then displaced by a distance $\Delta d,$ and the number of fringes produced by each laser and shifting past a reference point (a photo detector) is counted. In a given wavelength meter, a red He-Ne laser $\left(\lambda_{\mathrm{Red}}=632.8 \mathrm{nm}\right)$ is used as a reference laser. When the movable mirror of the interferometer is displaced by a distance $\Delta d$, the shifting of $\Delta N_{\mathrm{Red}}=6.000 \cdot 10^{4}$ red fringes and $\Delta N_{\text {unknown }}=7.780 \cdot 10^{4}$ fringes is observed by the photo detector.
a) Calculate the wavelength of the unknown laser.
b) Calculate the displacement, $\Delta d$, of the movable mirror.

Ajay Singhal

Numerade Educator

Problem 39

Monochromatic blue light $(\lambda=449 \mathrm{nm})$ is beamed into a Michelson interferometer. How many fringes shift on the screen when the movable mirror is moved a distance $d=0.381 \mathrm{~mm} ?$

Narayan Hari

Numerade Educator

Problem 40

At the Long-baseline Interferometer Gravitational-wave Observatory (LIGO) facilities in Hanford, Washington, and Livingston, Louisiana, laser beams of wavelength $550.0 \mathrm{nm}$ travel along perpendicular paths $4.000 \mathrm{~km}$ long. Each beam is reflected along its path and back 100 times before the beams are combined and compared. If a gravitational wave increases the length of one path and decreases the other, each by 1.000 part in $10^{21}$, what is the resulting phase difference between the two beams?

Narayan Hari

Numerade Educator

Problem 41

Light of wavelength $653 \mathrm{nm}$ illuminates a single slit. If the angle between the first dark fringes on either side of the central maximum is $32.0^{\circ},$ what is the width of the slit?

Narayan Hari

Numerade Educator

Problem 42

An instructor uses light of wavelength $633 \mathrm{nm}$ to create a diffraction pattern with a slit of width $0.135 \mathrm{~mm} .$ How far away from the slit must the instructor place the screen in order for the full width of the central maximum to be $5.00 \mathrm{~cm} ?$

Narayan Hari

Numerade Educator

Problem 43

What is the largest slit width for which there are no minima when the wavelength of the incident light on the single slit is $600 . \mathrm{nm} ?$

Narayan Hari

Numerade Educator

Problem 44

Plane microwaves are incident on a single slit of width $2.00 \mathrm{~cm}$. The second minimum is observed at an angle of $43.0^{\circ} .$ What is the wavelength of the microwaves? $?$ ? microwave??

Narayan Hari

Numerade Educator

Problem 45

The Large Binocular Telescope (LBT), on Mount Graham near Tucson, Arizona, has two 8.4 -m-diameter primary mirrors. The mirrors are centered a distance of $14.4 \mathrm{~m}$ apart, thus producing a mirror with an effective diameter of $14.4 \mathrm{~m} .$ What is the minimum angular resolution of the LBT for green light $(\lambda=550 \mathrm{nm}) ?$.

Narayan Hari

Numerade Educator

Problem 46

A canvas tent has a single, tiny hole in its side. On the opposite wall of the tent, $2.0 \mathrm{~m}$ away, you observe a dot (due to sunlight incident upon the hole) of width $2.0 \mathrm{~mm}$, with a faint ring around it. What is the size of the hole in the tent? (Assume a wave length of $570 \mathrm{nm}$ for the sunlight.)

Narayan Hari

Numerade Educator

Problem 47

Calculate and compare the angular resolutions of the Hubble Space Telescope (aperture diameter, $2.40 \mathrm{~m}$; wavelength, $450 . \mathrm{nm}$ ), the Keck Telescope (aperture diameter, $10.0 \mathrm{~m}$; wavelength, $450 . \mathrm{nm})$, and the Arecibo radio telescope (aperture diameter, $305 \mathrm{~m}$; wavelength, $0.210 \mathrm{~m}$ ). Assume that the resolution of each instrument is limited by diffraction.

Ajay Singhal

Numerade Educator

Problem 48

The Hubble Space Telescope is capable of resolving optical images to an angular resolution of $2.80 \cdot 10^{-7}$ rad with its 2.40 -m mirror (see Figure 34.33). How large would a radio telescope have to be in order to image an object with the same resolution, assuming that the wavelength of the radio waves emitted by the object is $10.0 \mathrm{~cm} ?$.

Narayan Hari

Numerade Educator

Problem 49

Think of the pupil of your eye as a circular aperture $5.00 \mathrm{~mm}$ in diameter. Assume you are viewing light of wavelength $550 . \mathrm{nm},$ to which your eyes are maximally sensitive.
a) What is the minimum angular separation at which you can distinguish two stars?
b) What is the maximum distance at which you can distinguish the two headlights of a car mounted $1.50 \mathrm{~m}$ apart?

Narayan Hari

Numerade Educator

Problem 50

A red laser pointer shines light with a wavelength of $635 \mathrm{nm}$ on a double slit, producing a diffraction pattern on a screen that is $1.60 \mathrm{~m}$ behind the double slit. The central maximum of the diffraction pattern has a width of $4.20 \mathrm{~cm}$, and the fourth bright spot is missing on both sides. What is the width of the individual slits, and what is the separation between them?

Ajay Singhal

Numerade Educator

Problem 51

A double slit is opposite the center of a 1.8 -m-wide screen that is $2.0 \mathrm{~m}$ away. The slit separation is $24 \mu \mathrm{m},$ and the width of each slit is $7.2 \mu \mathrm{m} .$ How many bright fringes are visible on the screen, including the central maximum, if the slit is illuminated by $600 .-\mathrm{nm}$ light?

Ajay Singhal

Numerade Educator

Problem 52

A two-slit apparatus is covered with a red $(670-\mathrm{nm})$ filter. When white light shines on the filter, nine interference maxima appear on a screen, within the 4.50 -cm-wide central diffraction maximum. When a blue $(450-\mathrm{nm})$ filter replaces the red filter, how many interference maxima will there be in the central diffraction maximum, and how wide will that diffraction maximum be?

Narayan Hari

Numerade Educator

Problem 53

The intensity pattern observed in a two-slit experiment is presented in the figure. The red line represents the actual intensity measured as a function of angle, while the green line represents the envelope of the single-slit interference pattern.
a) Determine the slit width $a$ in terms of the wavelength $\lambda$ of the light used in the experiment.
b) Determine the center-to-center slit separation $d$ in terms of the wavelength $\lambda$
c) Using the information in the graph, determine the ratio of slit width $a$ to the center-to-center separation between the slits, $d$.
d) Can you calculate the wavelength of light, actual slit separation, and slit width?

Ajay Singhal

Numerade Educator

Problem 54

Two different wavelengths of light are incident on a diffraction grating. One wavelength is $600 . \mathrm{nm}$, and the other is unknown. If the third-order bright fringe of the unknown wavelength appears at the same position as the second-order bright fringe of the $600 .-\mathrm{nm}$ light, what is the value of the unknown wavelength?

Narayan Hari

Numerade Educator

Problem 55

Light from an argon laser strikes a diffraction grating that has 7020 slits per centimeter. The central and first-order maxima are separated by $0.332 \mathrm{~m}$ on a wall $1.00 \mathrm{~m}$ from the grating. Determine the wavelength of the laser light.

Narayan Hari

Numerade Educator

Problem 56

A 5.000-cm-wide diffraction grating with 200 slits is used to resolve two closely spaced lines (a doublet) in a spectrum. The doublet consists of two wavelengths, $\lambda_{\mathrm{a}}=629.8 \mathrm{nm}$ and $\lambda_{\mathrm{b}}=630.2 \mathrm{nm} .$ The light illuminates the entire grating at normal incidence. Calculate to four significant digits the angles $\theta_{1 \mathrm{a}}$ and $\theta_{\mathrm{lb}}$ with respect to the normal at which the first-order diffracted beams for the two wavelengths, $\lambda_{\mathrm{a}}$ and $\lambda_{\mathrm{b}}$, respectively, will be reflected from the grating. Note that this is not $0^{\circ} !$ What order of diffraction is required to resolve these two lines using this grating?

Ajay Singhal

Numerade Educator

Problem 57

A diffraction grating has $4.00 \cdot 10^{3}$ slits/cm and has white light $(400 .-700 . \mathrm{nm})$ incident on it. What wavelength(s) will be visible at $45.0^{\circ} ?$

Ajay Singhal

Numerade Educator

Problem 58

What is the wavelength of the X-rays if first-order Bragg diffraction is observed at $23.0^{\circ}$ relative to the crystal surface, with an interatomic distance of $0.256 \mathrm{nm} ?$

Narayan Hari

Numerade Educator

Problem 59

How many slits per centimeter must a grating have if there are to be no second-order maxima or minima for any visible wavelength $(400 .-700 . \mathrm{nm}) ?$

Narayan Hari

Numerade Educator

Problem 60

Many times, radio antennas occur in pairs. They then produce constructive interference in one direction while producing destructive interference in another direction-acting as a directional antenna-so that their emissions don't overlap with nearby stations. How far apart at a minimum should a local radio station, operating at $88.1 \mathrm{MHz},$ place its pair of antennas operating in phase so that no emission occurs along a line $45.0^{\circ}$ from the line joining the antennas?

Narayan Hari

Numerade Educator

Problem 61

A laser produces a coherent beam of light that does not spread (diffract) as much in comparison to light from other sources, like an incandescent bulb. Lasers therefore have been used for very accurate measurements of large distances, such as the distance between the Moon and the Earth. In one such experiment, a laser pulse (wavelength of $633 \mathrm{nm})$ is fired at the Moon. What should be the size of the circular aperture of the laser source in order to produce a central maximum of 1.00 -km diameter on the surface of the Moon? The distance between the Moon and the Earth is $3.84 \cdot 10^{5} \mathrm{~km}$

Narayan Hari

Numerade Educator

Problem 62

A diffraction grating with exactly 1000 slits per centimeter is illuminated by a He-Ne laser of wavelength $633 \mathrm{nm} .$
a) What is the highest order of diffraction that could be observed with this grating?
b) What would be the highest order if there were exactly 10,000 slits per centimeter?

Ajay Singhal

Numerade Educator

Problem 63

The thermal stability of a Michelson interferometer can be improved by submerging it in water. Consider an interferometer that is submerged in water, measuring light from a monochromatic source that is in air. If the movable mirror moves a distance $d=0.200 \mathrm{~mm},$ exactly $N=800$ fringes are shifted on the screen. What is the original wavelength (in air) of the monochromatic light?

Narayan Hari

Numerade Educator

Problem 64

A Blu-ray player uses a blue laser that produces light with a wavelength in air of $405 \mathrm{nm}$. If the disc is protected with polycarbonate $(n=1.58)$, determine the minimum thickness of the disc for destructive interference. Compare this value to that for CDs illuminated by infrared light.

Narayan Hari

Numerade Educator

Problem 65

An airplane is made invisible to radar by coating it with a 5.00 -mm-thick layer of an antireflective polymer with index of refraction $n=1.50 .$ What is the wavelength of the radar waves for which the plane is made invisible?

Narayan Hari

Numerade Educator

Problem 66

Coherent monochromatic light passes through parallel slits and then onto a screen that is at a distance $L=2.40 \mathrm{~m}$ from the slits. The narrow slits are a distance $d=2.00 \cdot 10^{-5} \mathrm{~m}$ apart. If the minimum spacing between bright spots is $y=6.00 \mathrm{~cm},$ find the wavelength of the light.

Narayan Hari

Numerade Educator

Problem 67

Determine the minimum thickness of a soap film $(n=1.32)$ that would produce constructive interference when illuminated by light of wavelength $550 . \mathrm{nm}$

Narayan Hari

Numerade Educator

Problem 68

You are making a diffraction grating that is to be used to resolve the two spectral lines in the sodium $D$ doublet, at wavelengths of $588.9950 \mathrm{nm}$ and $589.5924 \mathrm{nm}$, by at least $2.00 \mathrm{~mm}$ on a screen that is $80.0 \mathrm{~cm}$ from the grating. The rulings are to cover a distance of $1.50 \mathrm{~cm}$ on the grating. What is the minimum number of rulings you should have on the grating?

Ajay Singhal

Numerade Educator

Problem 69

A Michelson interferometer is illuminated with a 600.-nm light source. How many fringes are observed to shift if one of the mirrors of the interferometer is moved a distance of $200 . \mu \mathrm{m} ?$

Narayan Hari

Numerade Educator

Problem 70

What is the smallest object separation you can resolve with your naked eye? Assume that the diameter of your pupil is $3.5 \mathrm{~mm}$ and that your eye has a near point of $25 \mathrm{~cm}$ and a far point of infinity.

Narayan Hari

Numerade Educator

Problem 71

With a telescope with an objective of diameter $12.0 \mathrm{~cm}$, how close can two features on the Moon be and still be resolved? Take the wavelength of the light to be $550 . \mathrm{nm}$, near the center of the visible spectrum.

Ajay Singhal

Numerade Educator

Problem 72

There is air on both sides of a soap film. What is the smallest thickness that the soap film $(n=1.420)$ can have and appear dark if illuminated with 500.-nm light?

Ajay Singhal

Numerade Educator

Problem 73

X-rays with a wavelength of $1.00 \mathrm{nm}$ are scattered off two small tumors in a human body. If the two tumors are a distance of $10.0 \mathrm{~cm}$ away from the X-ray detector, which has an entrance aperture of diameter $1.00 \mathrm{~mm}$, what is the minimum separation between the two tumors that will allow the X-ray detector to determine that there are two tumors instead of one?

Ajay Singhal

Numerade Educator

Problem 74

Glass with an index of refraction of 1.50 is inserted into one arm of a Michelson interferometer that uses a 600.-nm light source. This causes the fringe pattern to shift by exactly 1000 fringes. How thick is the glass?

Narayan Hari

Numerade Educator

Problem 75

White light is shone on a very thin layer of mica $(n=1.57)$, and above the mica layer, interference maxima for light of two wavelengths (and no other in between) are seen: $516.9 \mathrm{nm}$ and $610.9 \mathrm{nm}$. What is the thickness of the mica layer?

Ajay Singhal

Numerade Educator

Problem 76

A Newton's ring apparatus consists of a convex lens with a large radius of curvature $R$ placed on a flat glass disc. (a) Show that the horizontal distance $x$ from the center, the thickness $d$ of the air gap, and the radius of curvature $R$ are related by $x^{2}=2 R d$. (b) Show that the radius of the $n$ th constructive interference ring is given by $x_{n}=\left[\left(n+\frac{1}{2}\right) \lambda R\right]^{1 / 2}$.
(c) How many bright rings may be seen if the apparatus is illuminated by red light of wavelength $700 . \mathrm{nm}$ with $R=10.0 \mathrm{~m}$ and the plane glass disc diameter $5.00 \mathrm{~cm} ?$

Ajay Singhal

Numerade Educator

Problem 77

In a double-slit experiment, the slits are $2.49 \cdot 10^{-5} \mathrm{~m}$ apart. If light of wavelength $477 \mathrm{nm}$ passes through the slits, what will be the distance between the third-order and fourth-order bright fringes on a screen $1.23 \mathrm{~m}$ away?

Narayan Hari

Numerade Educator

Problem 78

In a double-slit experiment, the slits are $3.41 \cdot 10^{-5} \mathrm{~m}$ apart. The distance between the second-order and third-order bright fringes on a screen $1.63 \mathrm{~m}$ away is $2.30 \mathrm{~cm} .$ What is the wavelength of the light?

Ajay Singhal

Numerade Educator

Problem 79

A double-slit experiment using light of wavelength $485 \mathrm{nm}$ produces an interference pattern on a screen that is $2.01 \mathrm{~m}$ away from the slits. The distance between the first-order and third-order maxima on the screen is measured to be $4.50 \mathrm{~cm}$. What is the separation between the slits?

Ajay Singhal

Numerade Educator

Problem 80

A double-slit experiment using light of wavelength $489 \mathrm{nm}$ produces an interference pattern on a screen. The slit separation is $1.25 \cdot 10^{-2} \mathrm{~mm}$. The distance between the first-order and fourth-order maxima on the and the screen?

Ajay Singhal

Numerade Educator

Problem 81

The single-slit diffraction pattern shown in the figure was produced with light of wavelength $495 \mathrm{nm}$. The screen on which the pattern was projected is located a distance of $2.77 \mathrm{~m}$ from the slit. The slit has a width of $2.73 \mathrm{~mm}$. What is the width $w$ of the central maximum?

Ajay Singhal

Numerade Educator

Problem 82

The single-slit diffraction pattern shown in the figure was produced with light from a laser. The screen on which the pattern was projected is located a distance of $3.17 \mathrm{~m}$ from the slit. The slit has a width of $0.555 \mathrm{~mm}$. The width of the central maximum is $w=5.81 \mathrm{~mm}$. What is the wavelength of the laser light?

Ajay Singhal

Numerade Educator

Problem 83

The single-slit diffraction pattern shown in the figure was produced with light of wavelength $503 \mathrm{nm}$. The screen on which the pattern was projected is located a distance of $3.55 \mathrm{~m}$ from the slit. The width of the central maximum is $w=5.71 \mathrm{~mm}$. What is the width of the slit?

Ajay Singhal

Numerade Educator

Problem 84

The single-slit diffraction pattern shown in the figure was produced with light of wavelength $507 \mathrm{nm}$ incident on a slit of width $0.693 \mathrm{~mm} .$ The width of the central maximum is $w=5.75 \mathrm{~mm} .$ How far is the screen on which the pattern was projected from the slit?

Ajay Singhal

Numerade Educator