Q: In Young’s double-slit experiment, red light of wavelength $$\lambda = 664\ \text{nm}$$ passes through slits separated by $$d = 1.20 \times 10$$^{-4}$$\ \text{m}$$, and the screen is $$L = 2.75\ \text{m}$$ away. What is the distance on the screen between the central bright fringe and the third-order bright fringe?

$$y = m \frac{\lambda L}{d} = 3 \frac{664 \times 10$$^{-9}$$ \times 2.75}{1.20 \times 10$$^{-4}$$} = 0.0456\ \text{m}$$

Q: A diffraction grating has $$1.0 \times 10^4$ lines/cm. What is the slit separation d$ in meters?

$$d = 1.0 \times 10$$^{-6}$$\ \text{m}$$

Q: A thin film of gasoline ($$n = 1.40) on $$water ($$n = 1.33) $$appears yellow because destructive interference eliminates blue light ($$\lambda = 469\ \text{nm} in $$vacuum). What is the minimum non-zero thickness $$t of $$the film for this to occur?

$$t = \frac{\lambda_{\text{film}}}{2} = \frac{469\ \text{nm}/1.40}{2} = 168\ \text{nm}$$

Q: X-ray diffraction from a crystal with interatomic spacing $$d$$ produces a first-order maximum at angle $$\theta. $$Which equation allows you to solve for $$d$$?

$$d = \frac{m \lambda}{2 \sin \theta}$$

Q: A lens is coated with an anti-reflective film of index $$n_c = 1.234 to $$minimize reflection of yellow light ($$\lambda = 580\ \text{nm} in $$vacuum). What is the minimum thickness $$t of $$the coating?

$$t = \frac{\lambda}{4 n_c} = \frac{580}{4 \times 1.234} = 118\ \text{nm}$$

Q: In a single-slit diffraction experiment, the angle to the first minimum is $$4.7^\circ$$, the slit width is $$W = 5.0 \times 10$$^{-6}$$\ \text{m}$$, and the screen is $$L = 0.40\ \text{m}$$ away. What is the width $$2y of $$the central bright fringe?

$$2y = 2L \tan \theta = 2 \times 0.40 \times \tan 4.7^\circ = 0.066\ \text{m}$$

Question 1

In Young’s double-slit experiment, red light of wavelength $$\lambda = 664\ 	ext{nm}$$ passes through slits separated by $$d = 1.20 	imes 10$$^{-4}$$\ 	ext{m}$$, and the screen is $$L = 2.75\ 	ext{m}$$ away. What is the distance on the screen between the central bright fringe and the third-order bright fringe?

Accepted Answer

$$y = m \frac{\lambda L}{d} = 3 \frac{664 	imes 10$$^{-9}$$ 	imes 2.75}{1.20 	imes 10$$^{-4}$$} = 0.0456\ 	ext{m}$$

Question 2

Which equation gives the angular position $$	heta of $$the $$m-th $$order bright fringe in a double-slit interference pattern?

Accepted Answer

$$d \sin 	heta = m \lambda$$

Question 3

A single-slit diffraction pattern is observed on a screen. If the slit width $$W is $$decreased, what happens to the width of the central bright fringe?

Accepted Answer

The width of the central bright fringe increases.

Question 4

For a single-slit diffraction pattern, the angle $$	heta to $$the first dark fringe is given by which equation?

Accepted Answer

$$W \sin 	heta = \lambda$$

Question 5

A diffraction grating has $$1.0 	imes 10^4$ lines/cm. What is the slit separation d$ in meters?

Accepted Answer

$$d = 1.0 	imes 10$$^{-6}$$\ 	ext{m}$$

Question 6

Which of the following best explains why the bright fringes produced by a diffraction grating are much narrower than those produced by a double slit?

Accepted Answer

A diffraction grating has many slits, causing more constructive and destructive interference, which narrows the maxima.

Question 7

A thin film of gasoline ($$n = 1.40) on $$water ($$n = 1.33) $$appears yellow because destructive interference eliminates blue light ($$\lambda = 469\ 	ext{nm} in $$vacuum). What is the minimum non-zero thickness $$t of $$the film for this to occur?

Accepted Answer

$$t = \frac{\lambda_{	ext{film}}}{2} = \frac{469\ 	ext{nm}/1.40}{2} = 168\ 	ext{nm}$$

Question 8

Which equation describes the condition for constructive interference (principal maxima) in a diffraction grating?

Accepted Answer

$$d \sin 	heta = m \lambda$$

Question 9

X-ray diffraction from a crystal with interatomic spacing $$d$$ produces a first-order maximum at angle $$	heta. $$Which equation allows you to solve for $$d$$?

Accepted Answer

$$d = \frac{m \lambda}{2 \sin 	heta}$$

Question 10

A lens is coated with an anti-reflective film of index $$n_c = 1.234 to $$minimize reflection of yellow light ($$\lambda = 580\ 	ext{nm} in $$vacuum). What is the minimum thickness $$t of $$the coating?

Accepted Answer

$$t = \frac{\lambda}{4 n_c} = \frac{580}{4 	imes 1.234} = 118\ 	ext{nm}$$

Question 11

Why do soap bubbles and thin oil films appear multicolored and change color as you watch them?

Accepted Answer

The thickness of the film varies, causing constructive and destructive interference for different wavelengths at different locations.

Question 12

In a single-slit diffraction experiment, the angle to the first minimum is $$4.7^\circ$$, the slit width is $$W = 5.0 	imes 10$$^{-6}$$\ 	ext{m}$$, and the screen is $$L = 0.40\ 	ext{m}$$ away. What is the width $$2y of $$the central bright fringe?

Accepted Answer

$$2y = 2L 	an 	heta = 2 	imes 0.40 	imes 	an 4.7^\circ = 0.066\ 	ext{m}$$

Question 13

Which of the following is a real-world application of X-ray diffraction?

Accepted Answer

Determining the crystal structure of DNA.

Question 14

In thin film interference, what phase change occurs when light reflects from a medium with a higher refractive index?

Accepted Answer

A phase change equivalent to half a wavelength ($$\frac{\lambda}{2}) $$occurs.

Question 15

A mixture of violet ($$\lambda = 410\ 	ext{nm}) $$and red ($$\lambda = 660\ 	ext{nm}) $$light falls on a grating with $$1.0 	imes 10^4$ lines/cm. What is the angle $$	heta$$ for the first-order maximum for red light?

Accepted Answer

$$\sin 	heta = \frac{660 	imes 10$$^{-9}$$}{1.0 	imes 10$$^{-6}$$} = 0.66 \Rightarrow 	heta = 41^\circ$$

Question 16

Which of the following best describes the Poisson spot observed in a diffraction experiment with an opaque disk?

Accepted Answer

A bright spot at the center of the shadow due to constructive interference of diffracted waves.

Question 17

A crystal is bombarded with X-rays of wavelength $$0.0834\ 	ext{nm}$$, and the first diffraction maximum is observed at $$	heta = 13.2^\circ. $$What is the spacing $$d$$ between crystal planes?

Accepted Answer

$$d = \frac{0.0834 	imes 10$$^{-9}$$}{2 \sin 13.2^\circ} = 1.83 	imes 10$$^{-10}$$\ 	ext{m}$$

Lecture 19

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