Q: A ray of light passes from glass ($$n=1.50) $$into air ($$n=1.0003). $$What is the critical angle for total internal reflection?

$$\theta_c = \arcsin\left(\frac{n_2$}{n_1$}\right) = 41.8^\circ$$

Question 1

A beam of light passes from air into water at an angle of $$30^\circ$$ with respect to the normal. Using the indices of refraction from the provided table, what is the angle of refraction in the water?

Accepted Answer

$$22.0^\circ$$

Question 2

Which of the following best describes the condition for constructive interference in a double-slit experiment?

Accepted Answer

$$\Delta r = m \lambda$$, where $$m = 0, 1, 2, ...$$

Question 3

A solid sphere and a thin rod (about its center) have the same mass $$M$$ and radius $$R. $$Which has the greater moment of inertia and by what factor?

Accepted Answer

The thin rod, by a factor of $$2$$

Question 4

A sound wave travels through air and then through water. Given the bulk moduli and densities, which statement is correct about the speed of sound in these two media?

Accepted Answer

The speed of sound is greater in water because $$v = \sqrt{B/\rho}$$ and water has a much larger bulk modulus.

Question 5

A monochromatic light source is used in a double-slit experiment with slit separation $$d$$ and screen distance $$L. If $$the wavelength is doubled, what happens to the fringe spacing $$y_m$$?

Accepted Answer

It doubles, since $$y_m = m \lambda L / d$$

Question 6

A satellite orbits Earth at a distance $$r$$ from the center of the planet. According to Newton’s law of gravity, what happens to the gravitational force if the satellite’s distance is doubled?

Accepted Answer

The force decreases by a factor of 4

Question 7

A thin film of oil (n = 1.40) floats on water (n = 1.33). For constructive interference in the reflected light, what is the minimum nonzero thickness of the oil film for light of wavelength $$560\ \mathrm{nm} in $$air?

Accepted Answer

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

Question 8

Which of the following best describes the law of reflection?

Accepted Answer

$$	heta_r = 	heta_i$$

Question 9

A diffraction grating is used to separate light into its component wavelengths. If the number of lines per centimeter is increased, what happens to the angular separation between the first-order maxima for two close wavelengths?

Accepted Answer

The angular separation increases

Question 10

A planet orbits a star in a circular orbit. According to Kepler’s third law, if the orbital radius is increased by a factor of 4, by what factor does the orbital period change?

Accepted Answer

The period increases by a factor of 8

Question 11

A ray of light passes from glass ($$n=1.50) $$into air ($$n=1.0003). $$What is the critical angle for total internal reflection?

Accepted Answer

$$	heta_c = \arcsin\left(\frac{n_2$}{n_1$}ight) = 41.8^\circ$$

Question 12

A string of length $$L is $$fixed at both ends and vibrates in its third harmonic. What is the wavelength of the standing wave?

Accepted Answer

$$\lambda = \frac{2L}{3}$$

Question 13

A solid sphere and a spherical shell have the same mass $$M$$ and radius $$R. $$Which has the greater moment of inertia about its diameter?

Accepted Answer

The spherical shell, because $$I_{shell} = \frac{2}{3}MR^2$ and I$$_{sphere} = \frac{2}{5}$$MR^2$$

Question 14

A beam of white light passes through a glass prism. Which color is bent the most and why?

Accepted Answer

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

Question 15

A medical ultrasound device uses sound waves in the body. Why is the speed of sound in tissue (mostly water) much higher than in air?

Accepted Answer

Because water has a much higher bulk modulus than air

Question 16

A student observes a beat frequency of $$5\ \mathrm{Hz}$$ when two tuning forks are sounded together. If one fork has a frequency of $$256\ \mathrm{Hz}$$, what are the possible frequencies of the other fork?

Accepted Answer

$$251\ \mathrm{Hz} or$$ $$261\ \mathrm{Hz}$$

Question 17

A planet has twice the mass of Earth and the same radius. What is the acceleration due to gravity on its surface?

Accepted Answer

$$g' = 2g$$

Question 18

A laser beam in air strikes a diamond at $$45^\circ to $$the normal. Using the indices of refraction, what is the angle of refraction inside the diamond?

Accepted Answer

$$16.9^\circ$$

Question 19

Which of the following is NOT a valid assumption when applying the wave model of light to thin-film interference?

Accepted Answer

The film thickness is much greater than the wavelength of light

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