Q: A laser with wavelength $$\lambda = 500\ \mathrm{nm}$$ passes through two slits separated by $$d = 0.25\ \mathrm{mm}$$ and forms an interference pattern on a screen $$L = 2.0\ \mathrm{m}$$ away. What is the distance between adjacent bright fringes on the screen?

$$\Delta y = \dfrac{\lambda L}{d} = \dfrac{500 \times 10$$^{-9}$$\ \mathrm{m} \times 2.0\ \mathrm{m}}{0.25 \times 10$$^{-3}$$\ \mathrm{m}} = 4.0\ \mathrm{mm}$$

Q: A single-slit diffraction pattern is produced using a slit of width $$a = 0.10\ \mathrm{mm}$$ and light of wavelength $$\lambda = 600\ \mathrm{nm}. $$What is the angular position $$\theta of $$the first dark fringe?

$$a \sin \theta = \lambda \implies \sin \theta = \dfrac{\lambda}{a} = \dfrac{600 \times 10$$^{-9}$$}{0.10 \times 10$$^{-3}$$} = 0.006$$

Q: A diffraction grating has 5000 lines per centimeter. What is the slit spacing $$d in $$meters?

$$d = \dfrac{1}{5000\ \mathrm{cm}^{-1}} = 2.0 \times 10$$^{-6}$$\ \mathrm{m}$$

Q: A student shines a green laser ($$\lambda = 530\ \mathrm{nm}) on a $$human hair and observes a central maximum of width $$w = 14\ \mathrm{mm} on a $$screen $$L = 1.2\ \mathrm{m}$$ away. What is the thickness $$a of $$the hair?

$$a = \dfrac{2 \lambda L}{w} = \dfrac{2 \times 530 \times 10$$^{-9}$$ \times 1.2}{0.014} = 9.1 \times 10$$^{-5}$$\ \mathrm{m}$$

Question 1

Which phenomenon explains the colorful patterns seen in soap bubbles and oil slicks?

Accepted Answer

Thin-film interference

Question 2

A laser with wavelength $$\lambda = 500\ \mathrm{nm}$$ passes through two slits separated by $$d = 0.25\ \mathrm{mm}$$ and forms an interference pattern on a screen $$L = 2.0\ \mathrm{m}$$ away. What is the distance between adjacent bright fringes on the screen?

Accepted Answer

$$\Delta y = \dfrac{\lambda L}{d} = \dfrac{500 	imes 10$$^{-9}$$\ \mathrm{m} 	imes 2.0\ \mathrm{m}}{0.25 	imes 10$$^{-3}$$\ \mathrm{m}} = 4.0\ \mathrm{mm}$$

Question 3

Which of the following statements about the index of refraction $$n is $$correct?

Accepted Answer

It is defined as $$n = \dfrac{c}{v}$$, where $$c is $$the speed of light in vacuum and $$v is $$the speed of light in the material.

Question 4

A single-slit diffraction pattern is produced using a slit of width $$a = 0.10\ \mathrm{mm}$$ and light of wavelength $$\lambda = 600\ \mathrm{nm}. $$What is the angular position $$	heta of $$the first dark fringe?

Accepted Answer

$$a \sin 	heta = \lambda \implies \sin 	heta = \dfrac{\lambda}{a} = \dfrac{600 	imes 10$$^{-9}$$}{0.10 	imes 10$$^{-3}$$} = 0.006$$

Question 5

In Young’s double-slit experiment, what happens to the fringe spacing if the wavelength of light is increased while keeping all other parameters constant?

Accepted Answer

The fringe spacing increases.

Question 6

A diffraction grating has 5000 lines per centimeter. What is the slit spacing $$d in $$meters?

Accepted Answer

$$d = \dfrac{1}{5000\ \mathrm{cm}^{-1}} = 2.0 	imes 10$$^{-6}$$\ \mathrm{m}$$

Question 7

Which of the following best describes the effect of increasing the number of slits in a diffraction grating?

Accepted Answer

The bright fringes become narrower and brighter.

Question 8

A thin film of oil ($$n = 1.50) on $$water ($$n = 1.33) $$appears dark when illuminated with white light. What is the most likely explanation?

Accepted Answer

Destructive interference occurs due to a half-wavelength phase shift at the top surface.

Question 9

A student shines a green laser ($$\lambda = 530\ \mathrm{nm}) on a $$human hair and observes a central maximum of width $$w = 14\ \mathrm{mm} on a $$screen $$L = 1.2\ \mathrm{m}$$ away. What is the thickness $$a of $$the hair?

Accepted Answer

$$a = \dfrac{2 \lambda L}{w} = \dfrac{2 	imes 530 	imes 10$$^{-9}$$ 	imes 1.2}{0.014} = 9.1 	imes 10$$^{-5}$$\ \mathrm{m}$$

Question 10

Which of the following is NOT explained by the wave model of light?

Accepted Answer

Sharp-edged shadows

Question 11

A circular aperture of diameter $$D$$ produces a central maximum of diameter $$d_{max} on a $$screen a distance $$L$$ away. Which equation gives the width of the central maximum?

Accepted Answer

$$d_{max} = 2.44 \dfrac{\lambda L}{D}$$

Question 12

In a thin-film interference experiment, a film of thickness $$t$$ and index $$n is $$illuminated with light of wavelength $$\lambda in $$vacuum. For constructive interference with one reflective phase change, which condition must be satisfied?

Accepted Answer

$$2 n t = (m + \dfrac{1}{2}) \lambda$$

Question 13

A diffraction grating is used to separate two closely spaced wavelengths of light. What property of the grating is most important for resolving the two wavelengths?

Accepted Answer

The number of slits $$N$$

Question 14

Which of the following best describes Huygens’ Principle?

Accepted Answer

Each point on a wave front acts as a source of spherical wavelets.

Question 15

A laboratory experiment produces a double-slit interference pattern. If the screen is moved farther from the slits, what happens to the fringe spacing?

Accepted Answer

The fringes move farther apart.

Question 16

A film with thickness $$t$$ gives constructive interference for light with wavelength $$\lambda in $$the film. How much thicker would the film need to be to give destructive interference?

Accepted Answer

$$\dfrac{\lambda}{2}$$ thicker

Question 17

Which of the following is a real-world application of thin-film interference?

Accepted Answer

Antireflection coatings on eyeglasses

Question 18

If the slit width in a single-slit diffraction experiment is decreased, what happens to the width of the central maximum?

Accepted Answer

It increases.

Question 19

Which of the following is true about the frequency and wavelength of light as it passes from air into glass?

Accepted Answer

The frequency remains the same, but the wavelength decreases.

Chapter 17: Wave Optics – Mini-Textbook Study Notes

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