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Chapter Review

Chapter Review

Concept Items

17.1Understanding Diffraction and Interference

1.

Which behavior of light is indicated by an interference pattern?

1. ray behavior
2. particle behavior
3. corpuscular behavior
4. wave behavior
2.

Which behavior of light is indicated by diffraction?

1. wave behavior
2. particle behavior
3. ray behavior
4. corpuscular behavior

17.2Applications of Diffraction, Interference, and Coherence

3.
There is a principle related to resolution that is expressed by this equation.
$θ=λD$
State that principle in full.
1. Two images are just resolved when the center of the diffraction pattern of one image is directly over the center of the diffraction pattern of the other.
2. Two images are just resolved when the center of the diffraction pattern of one image is directly over the first maximum of the diffraction pattern of the other.
3. Two images are just resolved when the center of the diffraction pattern of one image is directly over the first minimum of the diffraction pattern of the other.
4. Two images are just resolved when the center of the diffraction pattern of one image is directly over the second minimum of the diffraction pattern of the other.
4.
A principle related to resolution states, “Two images are just resolved when the center of the diffraction pattern of one is directly over the first minimum of the diffraction pattern of the other.” Write the equation that expresses that principle.
1. $θ=1.22Dλ$
2. $θ=Dλ$
3. $θ=λD$
4. $θ=1.22λD$
5.

Which statement completes this resolution?
Two images are just resolved when —

1. The center of the diffraction pattern of one image is directly over the central maximum of the diffraction pattern of the other.
2. The center of the diffraction pattern of one image is directly over the central minimum of the diffraction pattern of the other
3. The center of the diffraction pattern of one image is directly over the first minimum of the diffraction pattern of the other
4. The center of the diffraction pattern of one is directly over the first maximum of the diffraction pattern of the other

Critical Thinking Items

17.1Understanding Diffraction and Interference

6.
Describe a situation in which bodies of water and a line of rocks could create a diffraction pattern similar to light passing through double slits. Include the arrangement of the rocks, the positions of the bodies of water, and the location of the diffraction pattern. Note the dimensions that are necessary for the production of the pattern.
1. When waves from a small body of water pass through two widely separated openings and enter a larger body of water, a diffraction pattern is produced that is similar tothe diffraction pattern formed by light passing through two slits. The width of each opening is larger than the size of the wavelength of the waves.
2. When waves from a large body of water pass through two narrow openings and enter a smaller body of water, a diffraction pattern is produced that is similar to the diffraction pattern formed by light passing through two slits. The widths and separation of the openings are similar to the size of the wavelength of the waves.
3. When waves from a small body of water pass through two wide openings and enter a larger body of water, a diffraction pattern is produced that is similar tothe diffraction pattern formed by light passing through two slits. The separation between the openings is similar to the size of the wavelength of the waves.
4. When waves from a large body of water pass through two wide openings and enter a smaller body of water, a diffraction pattern is produced that is similar to the diffraction pattern formed by light passing through two slits. The widths and separation of the openings are larger than the size of the wavelength of the waves.

17.2Applications of Diffraction, Interference, and Coherence

7.
For what type of electromagnetic radiation would a grating with spacing greater than 800 nm be useful as a spectroscopic tool?
1. It can be used to analyze spectra only in the infrared portion of the spectrum.
2. It can be used to analyze spectra in the entire visible portion of the electromagnetic
spectrum.
3. It can only be used to analyze spectra in the short‐wavelength visible.
4. It can only be used to analyze spectra in the short‐wavelength visible and ultraviolet.
8.
A beam of green light has a wavelength of $500nm$ in a vacuum and a wavelength of $331nm$ in Plexiglas. What is the refractive index of Plexiglas?
1. $1.12$
2. $1.25$
3. $1.51$
4. $4.53$

Problems

17.1Understanding Diffraction and Interference

9.

What is the distance between two slits that produce a diffraction pattern with the first minimum at an angle of 45.0° when 410-nm violet light passes through the slits?

1. 2,030 nm
2. 1,450 nm
3. 410 nm
4. 290 nm
10.

A breakwater at the entrance to a harbor consists of a rock barrier with a 50.0 − m -wide opening. Ocean waves with a 20.0-m wavelength approach the opening straight on. At what angle to the incident direction are the boats inside the harbor most protected against wave action?

1. 11.5°
2. 7.46°
3. 5.74°
4. 23.6°

17.2Applications of Diffraction, Interference, and Coherence

11.

A 500-nm beam of light passing through a diffraction grating creates its second band of constructive interference at an angle of 1.50°. How far apart are the slits in the grating?

1. 38,200 nm
2. 19,100 nm
3. 667 nm
4. 333 nm
12.

The range of the visible-light spectrum is 380 nm to 780 nm. What is the maximum number of lines per centimeter a diffraction grating can have and produce a complete first-order spectrum for visible light?

1. 26,300 lines/cm
2. 13,200 lines/cm
3. 6,410 lines/cm
4. 12,820 lines/cm

17.2Applications of Diffraction, Interference, and Coherence

13.

In this performance task you will create one- and two-slit diffraction and observe the interference patterns that result.

Materials
• A utility knife (a knife with a razor blade-like cutting edge)
• Aluminum foil
• A straight edge
• A strong, small light source or a laser pointer
• A tape measure
• A white wall
Procedure
1. Cut a piece of aluminum foil about 15 cm × 15 cm.
2. Use the utility knife and the straight edge to cut a straight slit several cm long in the center of the foil square.
3. With the room darkened, one partner shines the light through the slit and toward the wall. The other partner observes the pattern on the wall. The partner with the light changes the distance from the foil to the wall and the distance from the light to the foil.
4. When the sharpest, brightest pattern possible is obtained, the partner who is not holding the foil and light makes measurements.
5. Measure the perpendicular (shortest) distance from the slit to the wall, the distance from the center of the pattern to several of the dark bands, and the distance from the slit to the same dark bands.
6. Carefully make a second slit parallel to the first slit and 1 mm or less away.
7. Repeat steps 2 through 5, only this time measure the distances to bright bands.

NOTE—In your calculations, use 580 nm for $λλ$ if you used white light. If you used a colored laser pointer, look up the wavelength of the color. You may find it easier to calculate $θθ$ from its tangent rather than from its sine.

1. Which experiment gave the most distinct pattern—one or two slits?
2. What was the width of the single slit? Compare the calculated distance with the measured distance.
3. What was the distance between the two slits? Compare the calculated distance with the measured distance.