Q: The angular width of the central maximum in a single-slit diffraction pattern is approximately given by which expression?

$$\theta \approx \frac{\lambda}{W}$$

Question 1

A glass prism disperses white light into its constituent colors. Which color bends the most as it passes through the prism, and why?

Accepted Answer

Violet, because it has the shortest wavelength and highest index of refraction.

Question 2

Given the indices of refraction for Crown glass at various wavelengths, which equation correctly describes the relationship between the speed of light in the glass ($$v) $$and the index of refraction ($$n$$)?

Accepted Answer

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

Question 3

A beam of red light ($$\lambda = 660\ 	ext{nm}) $$and violet light ($$\lambda = 410\ 	ext{nm}) $$enter a Crown glass prism at the same angle. Using the table of indices of refraction, which light exits the prism at a greater angle from the original direction?

Accepted Answer

Violet light, because it has a higher index of refraction.

Question 4

Which equation represents Snell’s Law for the refraction of light at the boundary between two media?

Accepted Answer

$$n_1$$ \sin \$$theta_1$$ = $$n_2$$ \sin \$$theta_2$$

Question 5

In Young’s double-slit experiment, the distance between the central bright fringe and the third-order bright fringe is given by which formula?

Accepted Answer

$$y = m \frac{\lambda L}{d}$$

Question 6

A student observes colored fringes in Young’s double-slit experiment using white light. Why is the central fringe white?

Accepted Answer

All wavelengths constructively interfere at the center.

Question 7

Which of the following best explains why sound can be heard around a corner, but light cannot be seen around a corner in the same way?

Accepted Answer

Sound waves have longer wavelengths, leading to greater diffraction.

Question 8

The angular width of the central maximum in a single-slit diffraction pattern is approximately given by which expression?

Accepted Answer

$$	heta \approx \frac{\lambda}{W}$$

Question 9

In a double-slit experiment, what condition must be met for constructive interference to occur at a point on the screen?

Accepted Answer

The path difference must be an integer multiple of the wavelength: $$\Delta \ell = m \lambda$$

Question 10

A compound microscope has an objective lens with focal length $$f_o = 0.40\ 	ext{cm}$$, an eyepiece with focal length $$f_e = 3.0\ 	ext{cm}$$, and a tube length $$L = 20.0\ 	ext{cm}. If $$the near point $$N = 25\ 	ext{cm}$$, what is the approximate angular magnification?

Accepted Answer

$$M \approx -\frac{L N}{f_o f_e}$$

Question 11

Which phenomenon is responsible for the formation of rainbows in the atmosphere?

Accepted Answer

Dispersion and refraction of sunlight in water droplets.

Question 12

In the context of Huygens’ principle, what is a wavelet?

Accepted Answer

A spherically-outgoing wave from a point source.

Question 13

Which of the following best describes the effect of increasing the ratio $$\frac{\lambda}{W} in a $$single-slit diffraction experiment?

Accepted Answer

The extent of diffraction increases, causing the central maximum to widen.

Question 14

A telescope has an objective lens with focal length $$f_o = 985\ 	ext{mm}$$ and an eyepiece with focal length $$f_e = 5.00\ 	ext{mm}. $$What is the angular magnification?

Accepted Answer

$$M = -\frac{f_o}{f_e}$$

Question 15

Which property of light is primarily responsible for the separation of colors in a prism?

Accepted Answer

The variation of the index of refraction with wavelength (dispersion).

Question 16

In a double-slit experiment, why are red fringes farther from the central fringe than green fringes?

Accepted Answer

Red light has a longer wavelength, resulting in greater fringe separation.

Question 17

Which of the following best describes the principle of linear superposition?

Accepted Answer

The electric fields of two or more light waves combine algebraically at a given point.

Question 18

Which condition must be met for two sources to be considered coherent?

Accepted Answer

The waves they emit maintain a constant phase relation.

Question 19

A single-slit diffraction pattern is observed on a screen. What happens to the width of the central maximum if the slit width $$W is $$decreased while keeping the wavelength $$\lambda$$ constant?

Accepted Answer

The width of the central maximum increases.

lecture 18

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