Question 1

Red laser light passes through a single slit to form a diffraction pattern.If the width of the slit is increased by a factor of two, what happens to the width of the central maximum? Note: Assume that the angle $\theta$ is sufficiently small so that (sin $\theta$ is nearly equal to $\theta$.
A)The width of the central maximum increases by a factor of 4.
B)The width of the central maximum decreases by a factor of 2.
C)The width of the central maximum decreases by a factor of 4.
D)The width of the central maximum increases by a factor of 2.
E)The width of the central maximum does not change.

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Question 2

The table lists the range of wavelengths in vacuum corresponding to a given color.If light one illuminates a film that has a refractive index of 1.333 and thickness of 183 nm with white light, which color is missing from the light reflected from the film? 
A)red
B)yellow
C)blue
D)green
E)orange

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Question 3

A 4.0 × 10²-nm thick film of kerosene (n = 1.2) is floating on water.White light is normally incident on the film.What is the visible wavelength in air that has a maximum intensity after the light is reflected? Note: the visible wavelength range is 380 nm to 750 nm. A)380 nm B)420 nm C)480 nm D)530 nm E)601 nm

Accepted Answer

The maximum intensity of the reflected light occurs when the path difference between the reflected rays from the top and bottom surfaces of the film is equal to an integer multiple of the wavelength. This can be expressed as:

2nt = mλ

where n is the refractive index of the film (1.2), t is the thickness of the film (4.0 × 10^-9 m), m is an integer, and λ is the wavelength of the incident light in vacuum.

Solving for λ, we get:

λ = 2nt/m ≈ 480 nm (for m = 1)

Note that the wavelength of the light in air is slightly larger than λ in vacuum, but the difference is negligible for visible wavelengths. Therefore, the answer is C: 480 nm.

Question 4

Which one of the following statements best explains why the diffraction of sound is more apparent than the diffraction of light under most circumstances?
A)Sound requires a physical medium for propagation.
B)Sound waves are longitudinal, and light waves are transverse.
C)Light waves can be represented by rays while sound waves cannot.
D)The speed of sound in air is six orders of magnitude smaller than that of light.
E)The wavelength of light is considerably smaller than the wavelength of sound.

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Question 5

A Michelson interferometer is used to measure the wavelength of light emitted from a monochromatic source.As the adjustable mirror is slowly moved through a distance D_A = 0.0265 mm, an observer counts 411 alternations between bright and dark fields.What is the wavelength of the monochromatic light used in this experiment? A)193 nm B)227 nm C)258 nm D)346 nm E)369 nm

Accepted Answer

The number of bright and dark fringes observed in an interferometer can be given by the equation:

N = (2d/λ) + 1

where N is the number of fringes observed, d is the distance that the movable mirror is moved, and λ is the wavelength of light.

In this case, we have:

N = 411
d = 0.0265 mm = 2.65 x 10^-5 m

Substituting these values into the equation, we get:

411 = (2 x 2.65 x 10^-5 m) / λ + 1

Solving for λ, we get:

λ = (2 x 2.65 x 10^-5 m) / (411 - 1) = 258 nm

Therefore, the wavelength of the monochromatic light used in this experiment is 258 nm, so the answer is choice C.

Question 6

Diffraction occurs when light passes through a single slit.Rank the following three choices in decreasing order, according to the extent of the diffraction that occurs (largest diffraction first):  Note: The blue light referred to in choices A and C is the same wavelength.Also, the narrow slit referred to in choices A and B is the same width.
A)A, B, C
B)B, A, C
C)C, A, B
D)A, C, B
E)B, C, A

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Question 7

Light with a wavelength of 644 nm uniformly illuminates a single slit.What is the width of the slit if the first-order dark fringe is located at $\theta$ = 0.125°? A)9.42 × 10^-⁴ m B)7.60 × 10^-⁴ m C)4.71 × 10^-⁴ m D)3.80 × 10^-⁴ m E)2.95 × 10^-⁴ m

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Question 8

Monochromatic light of wavelength $\lambda$_film is normally incident on a soap film in air.In terms of the wavelength, what is the thickness of the thinnest film for which the intensity of the reflected light will be a maximum? A)($\lambda$_film/4) B)($\lambda$_film/2) C)(3 $\lambda$_film/4) D)($\lambda$_film) E)(3 $\lambda$_film/2)

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Question 9

Light of wavelength 600 nm is incident upon a single slit with width 4 × 10^-⁴ m.The figure shows the pattern observed on a screen positioned 2 m from the slits.Determine the distance s. A)0.002 m B)0.003 m C)0.004 m D)0.006 m E)0.008 m

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Question 10

A lens that has an index of refraction of 1.61 is coated with a non-reflective coating that has an index of refraction of 1.45.Determine the minimum thickness for the film if it is to be non-reflecting for light of wavelength 5.60 × 10²nm. A)1.93 × 10^-⁷ m B)3.86 × 10^-⁷ m C)4.83 × 10^-⁸ m D)9.66 × 10^-⁸ m E)8.69 × 10^-⁸ m

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Question 11

Light of wavelength 700.0 nm passes through a diffraction grating.The m = 0 and m = 1 bright spots are 6.0 cm apart on a screen positioned 2.0 m from the grating.What is the spacing between the slits in the grating?
A)23.3 mm
B)42.0 $\mu$m
C)46.7 $\mu$m
D)73.8 $\mu$m
E)124 $\mu$m

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Question 12

The table lists the range of wavelengths in vacuum corresponding to a given color.Which one of these colors will produce a diffraction pattern with the widest central maximum, assuming all other factors are equal? 
A)red
B)yellow
C)green
D)blue
E)violet

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Question 13

Light of wavelength 650 nm is incident normally upon a glass plate.The glass plate rests on top of a second plate so that they touch at one end and are separated by 0.0325 mm at the other end as shown in the figure.Which range of values contains the horizontal separation between adjacent bright fringes? 
A)1.1 mm to 1.4 mm
B)1.4 mm to 2.8 mm
C)2.8 mm to 4.2 mm
D)4.2 mm to 5.6 mm
E)5.6 mm to 7.0 mm

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Question 14

Light with a wavelength of 600.0 nm is incident on a single slit of width 6.5 $\mu$m.The resulting diffraction pattern is observed on a nearby screen and has a central maximum of width 3.5 m.What is the distance between the screen and the slit?
A)9.5 m
B)19 m
C)38 m
D)57 m
E)76 m

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Question 15

A monochromatic beam of microwaves with a wavelength of 0.052 m is directed at a rectangular opening of width 0.35 m.The resulting diffraction pattern is measured along a wall 8.0 m from the opening.What is the distance between the first- and second-order dark fringes?
A)1.3 m
B)1.8 m
C)2.1 m
D)2.5 m
E)3.7 m

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Question 16

Light of 600.0 nm is incident upon a single slit.The resulting diffraction pattern is observed on a screen that is 0.50 m from the slit.The distance between the first and third minima of the diffraction pattern is 0.80 mm.Which range of values listed below contains the width of the slit?
A)0.1 mm to 0.4 mm
B)0.4 mm to 0.8 mm
C)0.8 mm to 1.2 mm
D)1.2 mm to 1.6 mm
E)1.6 mm to 2.0 mm

Accepted Answer

The distance between the central maximum and the first minimum is given by

$sin(	heta) =  \frac{\lambda}{w}$,

where $	heta$ is the angle between the line from the center of the slit to the first minimum and the line from the center of the slit to the central maximum, $\lambda$ is the wavelength of light, and $w$ is the width of the slit.

For the third minimum, the angle is approximately twice as large as for the first minimum: $	heta \approx 2 sin^{-1}(\frac{1.22 \lambda}{w})$.

The distance between the first and third minima on the screen is given by

$y = Ltan(	heta) \approx L\frac{2 sin^{-1}(\frac{1.22 \lambda}{w})}{\sqrt{1-(\frac{1.22 \lambda}{w})^2}}$,

where L is the distance between the slit and the screen.

Plugging in the given values and solving for $w$, we get:

$w \approx 0.53	ext{ mm}$
 
Therefore, the width of the slit is between 0.4 mm and 0.8 mm, which is answer choice B.

Question 17

What is the minimum (non-zero) thickness of a benzene (n = 1.501) thin film that will result in constructive interference when viewed at normal incidence and illuminated with orange light ($\lambda$_vacuum = 615 nm)? A glass slide (n_g = 1.620) supports the thin film. A)51.0 nm B)306 nm C)204 nm D)102 nm E)76.0 nm

Accepted Answer

For constructive interference, the path difference between the reflected rays from the top and bottom surface of the thin film should be an integer multiple of the wavelength of the light. 
Path difference = 2nt where n is the refractive index of the thin film and t is its thickness. 
Thus, t = mλ/2n, where m is an integer. 
For orange light, λ = 615 nm and for benzene, n = 1.501. For constructive interference, m = 1. 
t = λ/2n = 204 nm. 
However, the thin film is supported by a glass slide, which also reflects some of the light. The additional path difference due to the reflection from the glass slide is λ/2. Thus, the total path difference should be an odd multiple of λ/2 for constructive interference. 
Total path difference = 2nt + λ/2 = (2n+1)λ/2. 
For m = 1, t = λ/2n = 204 nm. 
The additional path difference due to the glass slide is λ/2 = 307.5 nm. 
Thus, the minimum thickness of the benzene film that will result in constructive interference is given by: 
2nt + λ/2 = (2n+1)λ/2 = 922.5 nm. 
Solving for t, we get t = 307.5 nm - λ/2n = 204 nm. 
Therefore, the best choice is C: 204 nm.

Question 18

A transparent film (n = 1.4) is deposited on a glass lens (n = 1.5) to form a non-reflective coating.What thickness would prevent reflection of light with wavelength 5.00 × 10²nm in air? A)89 nm B)125 nm C)170 nm D)250 nm E)357 nm

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Question 19

Light of wavelength 625 nm passes through a single slit of width 0.320 mm and forms a diffraction pattern on a flat screen located 8.00 m away.Determine the distance between the middle of the central bright fringe and the first dark fringe.
A)0.156 cm
B)0.516 cm
C)1.56 cm
D)5.16 cm
E)6.51 cm

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Question 20

A portion of a soap bubble appears yellow ($\lambda$ = 588.0 nm in vacuum) when viewed at normal incidence in white light.Determine the two smallest, non-zero thicknesses for the soap film if its index of refraction is 1.40.
A)89 nm and 179 nm
B)89 nm and 268 nm
C)105 nm and 315 nm
D)125 nm and 375 nm.
E)170 nm and 536 nm

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Quiz 27: Interference and the Wave Nature of Light

Red laser light passes through a single slit to form a diffraction pattern.If the width of the slit is increased by a factor of two, what happens to the width of the central maximum? Note: Assume that the angle $\theta$ is sufficiently small so that (sin $\theta$ is nearly equal to $\theta$ .

A 4.0 × 10²-nm thick film of kerosene (n = 1.2) is floating on water.White light is normally incident on the film.What is the visible wavelength in air that has a maximum intensity after the light is reflected? Note: the visible wavelength range is 380 nm to 750 nm.

Which one of the following statements best explains why the diffraction of sound is more apparent than the diffraction of light under most circumstances?

Light with a wavelength of 644 nm uniformly illuminates a single slit.What is the width of the slit if the first-order dark fringe is located at $\theta$ = 0.125°?

Monochromatic light of wavelength $\lambda$ _film is normally incident on a soap film in air.In terms of the wavelength, what is the thickness of the thinnest film for which the intensity of the reflected light will be a maximum?

Light of wavelength 600 nm is incident upon a single slit with width 4 × 10^-⁴ m.The figure shows the pattern observed on a screen positioned 2 m from the slits.Determine the distance s.

A lens that has an index of refraction of 1.61 is coated with a non-reflective coating that has an index of refraction of 1.45.Determine the minimum thickness for the film if it is to be non-reflecting for light of wavelength 5.60 × 10²nm.

Light of wavelength 700.0 nm passes through a diffraction grating.The m = 0 and m = 1 bright spots are 6.0 cm apart on a screen positioned 2.0 m from the grating.What is the spacing between the slits in the grating?

Light with a wavelength of 600.0 nm is incident on a single slit of width 6.5 $\mu$ m.The resulting diffraction pattern is observed on a nearby screen and has a central maximum of width 3.5 m.What is the distance between the screen and the slit?

A monochromatic beam of microwaves with a wavelength of 0.052 m is directed at a rectangular opening of width 0.35 m.The resulting diffraction pattern is measured along a wall 8.0 m from the opening.What is the distance between the first- and second-order dark fringes?

Light of 600.0 nm is incident upon a single slit.The resulting diffraction pattern is observed on a screen that is 0.50 m from the slit.The distance between the first and third minima of the diffraction pattern is 0.80 mm.Which range of values listed below contains the width of the slit?

What is the minimum (non-zero) thickness of a benzene (n = 1.501) thin film that will result in constructive interference when viewed at normal incidence and illuminated with orange light ( $\lambda$ _vacuum = 615 nm) ? A glass slide (n_g = 1.620) supports the thin film.

A transparent film (n = 1.4) is deposited on a glass lens (n = 1.5) to form a non-reflective coating.What thickness would prevent reflection of light with wavelength 5.00 × 10²nm in air?

Light of wavelength 625 nm passes through a single slit of width 0.320 mm and forms a diffraction pattern on a flat screen located 8.00 m away.Determine the distance between the middle of the central bright fringe and the first dark fringe.

A portion of a soap bubble appears yellow ( $\lambda$ = 588.0 nm in vacuum) when viewed at normal incidence in white light.Determine the two smallest, non-zero thicknesses for the soap film if its index of refraction is 1.40.

Quiz 27: Interference and the Wave Nature of Light

Red laser light passes through a single slit to form a diffraction pattern.If the width of the slit is increased by a factor of two, what happens to the width of the central maximum? Note: Assume that the angle θ\thetaθ is sufficiently small so that (sin θ\thetaθ is nearly equal to θ\thetaθ .

The table lists the range of wavelengths in vacuum corresponding to a given color.If light one illuminates a film that has a refractive index of 1.333 and thickness of 183 nm with white light, which color is missing from the light reflected from the film?

A 4.0 × 102-nm thick film of kerosene (n = 1.2) is floating on water.White light is normally incident on the film.What is the visible wavelength in air that has a maximum intensity after the light is reflected? Note: the visible wavelength range is 380 nm to 750 nm.

Which one of the following statements best explains why the diffraction of sound is more apparent than the diffraction of light under most circumstances?

Light with a wavelength of 644 nm uniformly illuminates a single slit.What is the width of the slit if the first-order dark fringe is located at θ\thetaθ = 0.125°?

Monochromatic light of wavelength λ\lambdaλ film is normally incident on a soap film in air.In terms of the wavelength, what is the thickness of the thinnest film for which the intensity of the reflected light will be a maximum?

Light of wavelength 600 nm is incident upon a single slit with width 4 × 10-4 m.The figure shows the pattern observed on a screen positioned 2 m from the slits.Determine the distance s.

A lens that has an index of refraction of 1.61 is coated with a non-reflective coating that has an index of refraction of 1.45.Determine the minimum thickness for the film if it is to be non-reflecting for light of wavelength 5.60 × 102 nm.