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Test Prep

Multiple Choice

17.1 Understanding Diffraction and Interference

Which remains unchanged when a monochromatic beam of light passes from air into water?

the speed of the light
the direction of the beam
the frequency of the light
the wavelength of the light

Two slits are separated by a distance of 3500 nm . If light with a wavelength of 500 nm passes through the slits and produces an interference pattern, the m = ________ order minimum appears at an angle of 30.0°.

In the sunlight, the shadow of a building has fuzzy edges even if the building does not. Is this a diffraction effect? Explain.

This is a diffraction effect. The whole building acts as the origin for a new wavefront.
This is a diffraction effect. Every point on the edge of the building’s shadow acts as the origin for a new wavefront.
This is a refraction effect. The whole building acts as the origin for a new wavefront.
This is a refraction effect. Every point at the edge of the building’s shadow acts as the origin for a new wavefront.

17.2 Applications of Diffraction, Interference, and Coherence

Two images are just resolved when the center of the diffraction pattern of one is directly over ________ of the diffraction pattern of the other.

the center
the first minimum
the first maximum
the last maximum

Two point sources of

500 nm

light are just resolvable as they pass through a small hole. The angle to the first minimum of one source is

1.00 rad

. What is the diameter of the hole?

$410 nm$
$57.3 nm$
$10.6 nm$
$610 nm$

Will a beam of light shining through a 1-mm hole behave any differently than a beam of light that is 1 mm wide as it leaves its source? Explain.?

Yes, the beam passing through the hole will spread out as it travels, because it is diffracted by the edges of the hole, whereas the 1 -mm beam, which encounters no diffracting obstacle, will not spread out.
Yes, the beam passing through the hole will be made more parallel by passing through the hole, and so will not spread out as it travels, whereas the unaltered wavefronts of the 1-mm beam will cause the beam to spread out as it travels.
No, both beams will remain the same width as they travel, and they will not spread out.
No, both beams will spread out as they travel.

A laser pointer emits a coherent beam of parallel light rays. Does the light from such a source spread out at all? Explain.

Yes, every point on a wavefront is not a source of wavelets, which prevent the spreading of light waves.
No, every point on a wavefront is not a source of wavelets, so that the beam behaves as a bundles of rays that travel in their initial direction.
No, every point on a wavefront is a source of wavelets, which keep the beam from spreading.
Yes, every point on a wavefront is a source of wavelets, which cause the beam to spread out steadily as it moves forward.

Short Answer

17.1 Understanding Diffraction and Interference

Light passing through double slits creates a diffraction pattern. How would the spacing of the bands in the pattern change if the slits were closer together?

The bands would be closer together.
The bands would spread farther apart.
The bands would remain stationary.
The bands would fade and eventually disappear.

A beam of light passes through a single slit to create a diffraction pattern. How will the spacing of the bands in the pattern change if the width of the slit is increased?

The width of the spaces between the bands will remain the same.
The width of the spaces between the bands will increase.
The width of the spaces between the bands will decrease.
The width of the spaces between the bands will first decrease and then increase.

10.

What is the wavelength of light falling on double slits separated by

2.00 μ m

if the third-order maximum is at an angle of

{60.0}^{\circ}

$667 nm$
$471 nm$
$333 nm$
$577 nm$

11.

What is the longest wavelength of light passing through a single slit of width 1.20 μm for which there is a first-order minimum?

1.04 µm
0.849 µm
0.600 µm
2.40 µm

17.2 Applications of Diffraction, Interference, and Coherence

12.

Describe a diffraction grating and the interference pattern it produces.

A diffraction grating is a large collection of evenly spaced parallel lines that produces an interference pattern that is similar to but sharper and better dispersed than that of a double slit.
A diffraction grating is a large collection of randomly spaced parallel lines that produces an interference pattern that is similar to but less sharp or well-dispersed as that of a double slit.
A diffraction grating is a large collection of randomly spaced intersecting lines that produces an interference pattern that is similar to but sharper and better dispersed than that of a double slit.
A diffraction grating is a large collection of evenly spaced intersecting lines that produces an interference pattern that is similar to but less sharp or well-dispersed as that of a double slit.

13.

Suppose pure-wavelength light falls on a diffraction grating. What happens to the interference pattern if the same light falls on a grating that has more lines per centimeter?

The bands will spread farther from the central maximum.
The bands will come closer to the central maximum.
The bands will not spread farther than the first maximum.
The bands will come closer to the first maximum.

14.

How many lines per centimeter are there on a diffraction grating that gives a first-order maximum for 473 nm blue light at an angle of 25.0°?

529,000 lines/cm
50,000 lines/cm
851 lines/cm
8,934 lines/cm

15.

What is the distance between lines on a diffraction grating that produces a second-order maximum for 760-nm red light at an angle of 60.0°?

2.28 × 10⁴ nm
3.29 × 10² nm
2.53 × 10¹ nm
1.76 × 10³ nm

Extended Response

17.1 Understanding Diffraction and Interference

16.

Suppose you use a double slit to perform Young’s double-slit experiment in air, and then repeat the experiment with the same double slit in water. Does the color of the light change? Do the angles to the same parts of the interference pattern get larger or smaller? Explain.

No, the color is determined by frequency. The magnitude of the angle decreases.
No, the color is determined by wavelength. The magnitude of the angle decreases.
Yes, the color is determined by frequency. The magnitude of the angle increases.
Yes, the color is determined by wavelength. The magnitude of the angle increases.

17.

A double slit is located at a distance x from a screen, with the distance along the screen from the center given by y. When the distance d between the slits is relatively large, there will be numerous bright bands.

For small angles (where

\sin θ \approx θ

, with

θ

in radians), what is the distance between fringes?

$Δ y = \frac{d}{x λ}$
$Δ y = \frac{x d}{λ}$
$Δ y = \frac{λ}{x d}$
$Δ y = \frac{x λ}{d}$

17.2 Applications of Diffraction, Interference, and Coherence

18.

Compare the interference patterns of single-slit diffraction, double-slit diffraction, and a diffraction grating.

All three interference pattern produce identical bands.
A double slit produces the sharpest and most distinct bands.
A single slit produces the sharpest and most distinct bands.
The diffraction grating produces the sharpest and most distinct bands.

19.

An electric current through hydrogen gas produces several distinct wavelengths of visible light. The light is projected onto a diffraction grating having

10, 000

lines per centimeter. What are the wavelengths of the hydrogen spectrum if the light forms first-order maxima at angles of

{24.2}^{\circ}

{25.7}^{\circ}

{29.1}^{\circ}

, and

{41.0}^{\circ}

$λ_{1} = (10^{3} nm) \sin {24.2}^{\circ} = 410 nm$ $λ_{2} = (10^{3} nm) \sin {25.7}^{\circ} = 434 nm$ $λ_{3} = (10^{3} nm) \sin {29.1}^{\circ} = 486 nm$ $λ_{4} = (10^{3} nm) \sin {41.0}^{\circ} = 656 nm$
$λ_{1} = (10^{3} nm) \sin {41.0}^{\circ} = 410 nm$ $λ_{2} = (10^{3} nm) \sin {25.7}^{\circ} = 434 nm$ $λ_{3} = (10^{3} nm) \sin {29.1}^{\circ} = 486 nm$ $λ_{4} = (10^{3} nm) \sin {24.2}^{\circ} = 656 nm$
$λ_{1} = (10^{3} nm) \sin {24.2}^{\circ} = 410 nm$ $λ_{2} = (10^{3} nm) \sin {29.1}^{\circ} = 434 nm$ $λ_{3} = (10^{3} nm) \sin {25.7}^{\circ} = 486 nm$ $λ_{4} = (10^{3} nm) \sin {41.0}^{\circ} = 656 nm$
$λ_{1} = (10^{3} nm) \sin {41.0}^{\circ} = 410 nm$ $λ_{2} = (10^{3} nm) \sin {29.1}^{\circ} = 434 nm$ $λ_{3} = (10^{3} nm) \sin {25.7}^{\circ} = 486 nm$ $λ_{4} = (10^{3} nm) \sin {24.2}^{\circ} = 656 nm$

Test Prep

Multiple Choice

17.1 Understanding Diffraction and Interference

17.2 Applications of Diffraction, Interference, and Coherence

Short Answer

17.1 Understanding Diffraction and Interference

17.2 Applications of Diffraction, Interference, and Coherence

Extended Response

17.1 Understanding Diffraction and Interference

17.2 Applications of Diffraction, Interference, and Coherence

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