Q: A beam of light with wavelength $$\lambda = 500\ \mathrm{nm}$$ passes from air ($$n = 1.0) $$into glass ($$n = 1.5). $$What is the wavelength of the light inside the glass?

$$\lambda_{\text{glass}} = 333\ \mathrm{nm}$$

Q: A double-slit experiment uses light of wavelength $$600\ \mathrm{nm}$$, slit separation $$d = 0.5\ \mathrm{mm}$$, and screen distance $$L = 2.0\ \mathrm{m}. $$What is the distance between adjacent bright fringes on the screen?

$$\Delta y = \frac{\lambda L}{d} = \frac{600 \times 10$$^{-9}$$ \times 2.0}{0.5 \times 10$$^{-3}$$} = 2.4\ \mathrm{mm}$$

Q: A thin film of oil ($$n = 1.40) $$floats on water ($$n = 1.33). $$Light of wavelength $$560\ \mathrm{nm} in $$air is incident perpendicularly. What is the minimum nonzero thickness of oil for which there is strong reflection due to constructive interference?

$$t = \frac{\lambda}{4n} = \frac{560}{4 \times 1.40} = 100\ \mathrm{nm}$$

Question 1

Which of the following best describes the phenomenon of diffraction as observed with light waves?

Accepted Answer

Diffraction is the bending of light as it passes through a narrow opening, causing the wave to spread out behind the opening.

Question 2

A beam of light with wavelength $$\lambda = 500\ \mathrm{nm}$$ passes from air ($$n = 1.0) $$into glass ($$n = 1.5). $$What is the wavelength of the light inside the glass?

Accepted Answer

$$\lambda_{	ext{glass}} = 333\ \mathrm{nm}$$

Question 3

In Young’s double-slit experiment, the condition for constructive interference (bright fringes) on the screen is:

Accepted Answer

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

Question 4

A double-slit experiment uses light of wavelength $$600\ \mathrm{nm}$$, slit separation $$d = 0.5\ \mathrm{mm}$$, and screen distance $$L = 2.0\ \mathrm{m}. $$What is the distance between adjacent bright fringes on the screen?

Accepted Answer

$$\Delta y = \frac{\lambda L}{d} = \frac{600 	imes 10$$^{-9}$$ 	imes 2.0}{0.5 	imes 10$$^{-3}$$} = 2.4\ \mathrm{mm}$$

Question 5

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

Accepted Answer

The index of refraction determines the speed of light in a material by $$v = \frac{c}{n}.$$

Question 6

A thin film of oil ($$n = 1.40) $$floats on water ($$n = 1.33). $$Light of wavelength $$560\ \mathrm{nm} in $$air is incident perpendicularly. What is the minimum nonzero thickness of oil for which there is strong reflection due to constructive interference?

Accepted Answer

$$t = \frac{\lambda}{4n} = \frac{560}{4 	imes 1.40} = 100\ \mathrm{nm}$$

Question 7

In a diffraction grating experiment, what happens to the angular separation between the first-order maxima if the number of lines per millimeter on the grating is increased?

Accepted Answer

The angular separation increases.

Question 8

Which of the following best explains why the colors of a soap bubble appear so vivid?

Accepted Answer

The colors are due to thin-film interference, where different wavelengths interfere constructively or destructively depending on the film thickness.

Question 9

A scientist uses a diffraction grating to analyze the light from a distant star. What property of the star can be determined using this technique?

Accepted Answer

The chemical composition of the star, by measuring the wavelengths of emitted light.

Question 10

In thin-film interference, a phase change of $$\frac{1}{2}$$ wavelength occurs when:

Accepted Answer

Light reflects from a boundary where the index of refraction increases.

Question 11

A double-slit experiment is performed with green light instead of red light, keeping all other parameters the same. What happens to the spacing between the bright fringes?

Accepted Answer

The spacing decreases because green light has a shorter wavelength than red light.

Question 12

Which of the following is NOT a requirement for observing a clear double-slit interference pattern with light?

Accepted Answer

The screen must be placed very close to the slits.

Question 13

A laser beam passes through a single narrow slit and produces a diffraction pattern on a distant screen. If the slit width is decreased, what happens to the width of the central maximum?

Accepted Answer

The central maximum becomes wider.

Question 14

Which of the following equations gives the speed of light in a material with index of refraction $$n$$?

Accepted Answer

$$v = \frac{c}{n}$$

Question 15

In a double-slit experiment, the path-length difference between the two slits to a point on the screen is $$1.5\lambda. $$What type of interference occurs at this point?

Accepted Answer

Destructive interference

Question 16

A thin film of material with index $$n = 1.38 is $$used as an antireflection coating on glass ($$n = 1.55). $$For light of wavelength $$550\ \mathrm{nm} in $$air, what is the minimum thickness of the film that will minimize reflection?

Accepted Answer

$$t = \frac{\lambda}{4n} = \frac{550}{4 	imes 1.38} = 99.6\ \mathrm{nm}$$

Question 17

Which of the following is a key difference between the interference pattern produced by a double slit and that produced by a diffraction grating?

Accepted Answer

A diffraction grating produces much narrower and brighter fringes than a double slit.

Question 18

Why does the frequency of light not change as it passes from one medium to another?

Accepted Answer

The frequency is determined by the source and remains constant, while the speed and wavelength change.

Wave Optics: Interference, Diffraction, and Thin-Film Effects

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