# 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°.

- 0
- 1
- 2
- 3

- 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

- $410\phantom{\rule{thinmathspace}{0ex}}\text{nm}$
- $57.3\phantom{\rule{thinmathspace}{0ex}}\text{nm}$
- $10.6\phantom{\rule{thinmathspace}{0ex}}\text{nm}$
- $610\phantom{\rule{thinmathspace}{0ex}}\text{nm}$

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.

- 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

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

- 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.

- $667\phantom{\rule{thinmathspace}{0ex}}\text{nm}$
- $471\phantom{\rule{thinmathspace}{0ex}}\text{nm}$
- $333\phantom{\rule{thinmathspace}{0ex}}\text{nm}$
- $577\phantom{\rule{thinmathspace}{0ex}}\text{nm}$

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

- 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.

- 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.

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

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 × 10
^{4}nm - 3.29 × 10
^{2}nm - 2.53 × 10
^{1}nm - 1.76 × 10
^{3}nm

### Extended Response

#### 17.1 Understanding Diffraction and Interference

- 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.

- $\mathrm{\Delta}y=\frac{d}{x\lambda}$
- $\mathrm{\Delta}y=\frac{xd}{\lambda}$
- $\mathrm{\Delta}y=\frac{\lambda}{xd}$
- $\mathrm{\Delta}y=\frac{x\lambda}{d}$

#### 17.2 Applications of Diffraction, Interference, and Coherence

- 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.

- ${\lambda}_{1}=\left({10}^{3}\phantom{\rule{thinmathspace}{0ex}}\text{nm}\right)\mathrm{sin}{24.2}^{\circ}=410\phantom{\rule{thinmathspace}{0ex}}\text{nm}$ ${\lambda}_{2}=\left({10}^{3}\phantom{\rule{thinmathspace}{0ex}}\text{nm}\right)\mathrm{sin}{25.7}^{\circ}=434\phantom{\rule{thinmathspace}{0ex}}\text{nm}$ ${\lambda}_{3}=\left({10}^{3}\phantom{\rule{thinmathspace}{0ex}}\text{nm}\right)\mathrm{sin}{29.1}^{\circ}=486\phantom{\rule{thinmathspace}{0ex}}\text{nm}$ ${\lambda}_{4}=\left({10}^{3}\phantom{\rule{thinmathspace}{0ex}}\text{nm}\right)\mathrm{sin}{41.0}^{\circ}=656\phantom{\rule{thinmathspace}{0ex}}\text{nm}$
- ${\lambda}_{1}=\left({10}^{3}\phantom{\rule{thinmathspace}{0ex}}\text{nm}\right)\mathrm{sin}{41.0}^{\circ}=410\phantom{\rule{thinmathspace}{0ex}}\text{nm}$ ${\lambda}_{2}=\left({10}^{3}\phantom{\rule{thinmathspace}{0ex}}\text{nm}\right)\mathrm{sin}{25.7}^{\circ}=434\phantom{\rule{thinmathspace}{0ex}}\text{nm}$ ${\lambda}_{3}=\left({10}^{3}\phantom{\rule{thinmathspace}{0ex}}\text{nm}\right)\mathrm{sin}{29.1}^{\circ}=486\phantom{\rule{thinmathspace}{0ex}}\text{nm}$ ${\lambda}_{4}=\left({10}^{3}\phantom{\rule{thinmathspace}{0ex}}\text{nm}\right)\mathrm{sin}{24.2}^{\circ}=656\phantom{\rule{thinmathspace}{0ex}}\text{nm}$
- ${\lambda}_{1}=\left({10}^{3}\phantom{\rule{thinmathspace}{0ex}}\text{nm}\right)\mathrm{sin}{24.2}^{\circ}=410\phantom{\rule{thinmathspace}{0ex}}\text{nm}$ ${\lambda}_{2}=\left({10}^{3}\phantom{\rule{thinmathspace}{0ex}}\text{nm}\right)\mathrm{sin}{29.1}^{\circ}=434\phantom{\rule{thinmathspace}{0ex}}\text{nm}$ ${\lambda}_{3}=\left({10}^{3}\phantom{\rule{thinmathspace}{0ex}}\text{nm}\right)\mathrm{sin}{25.7}^{\circ}=486\phantom{\rule{thinmathspace}{0ex}}\text{nm}$ ${\lambda}_{4}=\left({10}^{3}\phantom{\rule{thinmathspace}{0ex}}\text{nm}\right)\mathrm{sin}{41.0}^{\circ}=656\phantom{\rule{thinmathspace}{0ex}}\text{nm}$
- ${\lambda}_{1}=\left({10}^{3}\phantom{\rule{thinmathspace}{0ex}}\text{nm}\right)\mathrm{sin}{41.0}^{\circ}=410\phantom{\rule{thinmathspace}{0ex}}\text{nm}$ ${\lambda}_{2}=\left({10}^{3}\phantom{\rule{thinmathspace}{0ex}}\text{nm}\right)\mathrm{sin}{29.1}^{\circ}=434\phantom{\rule{thinmathspace}{0ex}}\text{nm}$ ${\lambda}_{3}=\left({10}^{3}\phantom{\rule{thinmathspace}{0ex}}\text{nm}\right)\mathrm{sin}{25.7}^{\circ}=486\phantom{\rule{thinmathspace}{0ex}}\text{nm}$ ${\lambda}_{4}=\left({10}^{3}\phantom{\rule{thinmathspace}{0ex}}\text{nm}\right)\mathrm{sin}{24.2}^{\circ}=656\phantom{\rule{thinmathspace}{0ex}}\text{nm}$