FIGURE Q33.1 shows light waves passing through two closely spaced, narrow slits. The graph shows the intensity of light on a screen behind the slits. Reproduce these graph axes, including the zero and the tick marks locating the double-slit fringes, then draw a graph to show how the light-intensity pattern will appear if the right slit is blocked, allowing light to go through only the left slit. Explain your reasoning.

FIGURE Q33.1

In a double-slit interference experiment, which of the following actions (perhaps more than one) would cause the fringe spacing to increase? (a) Increasing the wavelength of the light. (b) Increasing the slit spacing. (c) Increasing the distance to the viewing screen. (d) Submerging the entire experiment in water.

FIGURE Q33.3 shows the viewing screen in a double-slit experiment. Fringe C is the central maximum. What will happen to the fringe spacing if

1. The wavelength of the light is decreased?

2. The spacing between the slits is decreased?

3. The distance to the screen is decreased?

4. Suppose the wavelength of the light is 500 nm. How much farther is it from the dot on the screen in the center of fringe E to the left slit than it is from the dot to the right slit?

FIGURE Q33.3

Figure Q33.3 is the interference pattern seen on a viewing screen behind 2 slits. Suppose the 2 slits were replaced by 20 slits having the same spacing $d$ between adjacent slits.

1. Would the number of fringes on the screen increase, decrease, or stay the same?

2. Would the fringe spacing increase, decrease, or stay the same?

3. Would the width of each fringe increase, decrease, or stay the same?

4. Would the brightness of each fringe increase, decrease, or stay the same?

FIGURE Q33.5 shows the light intensity on a viewing screen behind a single slit of width $a$. The light’s wavelength is $\text{λ}$. Is $\text{λ}<a\text{,}\text{λ}=a\text{,}\text{λ}>a$, or is it not possible to tell? Explain.

FIGURE Q33.5

FIGURE Q33.6 shows the light intensity on a viewing screen behind a circular aperture. What happens to the width of the central maximum if

1. The wavelength of the light is increased?

2. The diameter of the aperture is increased?

3. How will the screen appear if the aperture diameter is less than the light wavelength?

FIGURE Q33.6

Narrow, bright fringes are observed on a screen behind a diffraction grating. The entire experiment is then immersed in water. Do the fringes on the screen get closer together, get farther apart, remain the same, or disappear? Explain.

1. Green light shines through a 100-mm-diameter hole and is observed on a screen. If the hole diameter is increased by 20%, does the circular spot of light on the screen decrease in diameter, increase in diameter, or stay the same? Explain.

2. Green light shines through a $100\text{-}\mu \text{m}$-diameter hole and is observed on a screen. If the hole diameter is increased by 20%, does the circular spot of light on the screen decrease in diameter, increase in diameter, or stay the same? Explain.

A Michelson interferometer using 800 nm light is adjusted to have a bright central spot. One mirror is then moved 200 nm forward, the other 200 nm back. Afterward, is the central spot bright, dark, or in between? Explain.

A Michelson interferometer is set up to display constructive interference (a bright central spot in the fringe pattern of Figure 33.25) using light of wavelength $\text{λ}$. If the wavelength is changed to $\text{λ}/2$, does the central spot remain bright, does the central spot become dark, or do the fringes disappear? Explain. Assume the fringes are viewed by a detector sensitive to both wavelengths.