Q: A diffraction grating has 5000 lines per centimeter. If monochromatic light of wavelength $$600\ \text{nm} is $$used, what is the angle for the first-order maximum?

Using $$d \sin \theta = m \lambda$$, $$d = \frac{1}{5000}\ \text{cm} = 2 \times 10$$^{-6}$$\ \text{m}$$, $$m=1$$, $$\sin \theta = \frac{600 \times 10$$^{-9}$$}{2 \times 10$$^{-6}$$} = 0.3$$, so $$\theta \approx 17.5^\circ.$$

Question 1

Which of the following best describes Huygens’ principle?

Accepted Answer

Every point on a wavefront acts as a source of spherical wavelets, and the new wavefront is tangent to their envelope.

Question 2

A highway mirage is observed on a hot day. Which physical principle explains this phenomenon?

Accepted Answer

Gradually changing index of refraction in heated air causes light to bend, as explained by Huygens’ principle.

Question 3

In Young’s double-slit experiment, what is the condition for constructive interference at a point on the screen?

Accepted Answer

The path difference between the two slits is an integer multiple of the wavelength: $$d \sin 	heta = m \lambda$$, where $$m is an $$integer.

Question 4

Why does a prism split white light into a rainbow of colors?

Accepted Answer

Because the index of refraction varies with wavelength, causing different colors to bend by different amounts (dispersion).

Question 5

A single-slit diffraction pattern is observed on a screen. What is the condition for the first minimum in the pattern?

Accepted Answer

The slit width $$a$$ and wavelength $$\lambda$$ satisfy $$a \sin 	heta = \lambda.$$

Question 6

A diffraction grating has 5000 lines per centimeter. If monochromatic light of wavelength $$600\ 	ext{nm} is $$used, what is the angle for the first-order maximum?

Accepted Answer

Using $$d \sin 	heta = m \lambda$$, $$d = \frac{1}{5000}\ 	ext{cm} = 2 	imes 10$$^{-6}$$\ 	ext{m}$$, $$m=1$$, $$\sin 	heta = \frac{600 	imes 10$$^{-9}$$}{2 	imes 10$$^{-6}$$} = 0.3$$, so $$	heta \approx 17.5^\circ.$$

Question 7

Which of the following statements about thin film interference is correct?

Accepted Answer

Interference occurs due to reflections from both the top and bottom surfaces of the film, and an extra half-wavelength shift occurs when light reflects from a medium with higher refractive index.

Question 8

A Michelson interferometer is used to measure the wavelength of light. If the movable mirror is shifted by $$0.25\ 	ext{mm}$$ and 500 fringes pass by, what is the wavelength of the light?

Accepted Answer

Each fringe corresponds to a path difference of $$\lambda$$, but the mirror moves $$\frac{\lambda}{2}$$ per fringe. So $$\lambda = \frac{2 	imes 0.25\ 	ext{mm}}{500} = 1.0 	imes 10$$^{-3}$$\ 	ext{mm} = 1000\ 	ext{nm}.$$

Question 9

What happens to the wavelength and frequency of light as it enters a medium with a higher index of refraction?

Accepted Answer

The frequency remains the same, but the wavelength decreases.

Question 10

Which of the following best explains why the sky appears blue during the day?

Accepted Answer

Shorter wavelengths (blue light) are scattered more efficiently by molecules in the atmosphere.

Question 11

A plane-polarized light beam passes through a polarizer whose axis makes an angle $$	heta$$ with the polarization direction. What is the transmitted intensity?

Accepted Answer

The transmitted intensity is $$I = I_0$ \cos^2$ 	heta.$$

Question 12

At Brewster’s angle, reflected light from a nonmetallic surface is completely polarized. What is the relationship between Brewster’s angle $$	heta_B$$ and the indices of refraction?

Accepted Answer

$$	an 	heta_B = \frac{n_2$}{n_1$}$$, where $$n_1 is $$the index of the initial medium and $$n_2 is $$the index of the second medium.

Question 13

Which of the following is NOT a requirement for observing interference in Young’s double-slit experiment?

Accepted Answer

The light must be polarized.

Question 14

A soap bubble appears colorful when viewed in sunlight. Which phenomenon is responsible for this effect?

Accepted Answer

Interference in thin films, where varying thickness causes constructive and destructive interference for different wavelengths.

Question 15

A spectrometer uses a diffraction grating to measure the wavelength of light. Which measurement is most critical for determining the wavelength?

Accepted Answer

The angle at which the light is diffracted.

Question 16

Which statement about liquid crystal displays (LCDs) is correct?

Accepted Answer

Applying an external voltage causes the liquid crystals to become polarized and block light, making the display appear dark.

Question 17

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

Accepted Answer

The width of the central maximum increases.

Question 18

Which of the following best describes the polarization of skylight?

Accepted Answer

Skylight is partially polarized due to scattering from molecules in the atmosphere, and the degree of polarization depends on the angle relative to the sun.

Chapter 24

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