Q: A thin film of oil (index of refraction $$n = 1.40) $$floats on water ($$n = 1.33). If $$white light is incident perpendicular to the film, what minimum thickness of oil will result in constructive interference for light of wavelength $$560\ \text{nm} in $$air?

$$t = \frac{560\ \text{nm}}{2 \times 1.40}$$

Q: A diffraction grating has $$d = 1.0 \times 10$$^{-6}$$\ \text{m}$$ between slits. What is the angle for the first-order maximum ($$m=1) $$for light of wavelength $$500\ \text{nm}$$?

$$\theta = \arcsin\left(\frac{500 \times 10$$^{-9}$$}{1.0 \times 10$$^{-6}$$}\right)$$

Q: A light ray in water ($$n = 1.33) $$strikes the water-air interface at $$60^\circ to $$the normal. Will total internal reflection occur?

Yes, because $$\sin \theta_c = \frac{n_2$}{n_1$}$$ and $$\theta_i \u003e \theta_c$$

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

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

Question 1

A thin film of oil (index of refraction $$n = 1.40) $$floats on water ($$n = 1.33). If $$white light is incident perpendicular to the film, what minimum thickness of oil will result in constructive interference for light of wavelength $$560\ 	ext{nm} in $$air?

Accepted Answer

$$t = \frac{560\ 	ext{nm}}{2 	imes 1.40}$$

Question 2

A solid sphere of mass $$M$$ and radius $$R$$ rolls without slipping down an incline. What is its moment of inertia about its center?

Accepted Answer

$$I = \frac{2}{5}MR^2$

Question 3

A diffraction grating has $$d = 1.0 	imes 10$$^{-6}$$\ 	ext{m}$$ between slits. What is the angle for the first-order maximum ($$m=1) $$for light of wavelength $$500\ 	ext{nm}$$?

Accepted Answer

$$	heta = \arcsin\left(\frac{500 	imes 10$$^{-9}$$}{1.0 	imes 10$$^{-6}$$}ight)$$

Question 4

A ray of light passes from air ($$n = 1.0003) $$into glass ($$n = 1.50) at an $$angle of $$30^\circ to $$the normal. What is the angle of refraction in the glass?

Accepted Answer

$$\$$theta_2$$ = \arcsin\left(\frac{n_1$ \sin \$$theta_1$$}{n_2$}\right)$$

Question 5

Which of the following best describes the law of reflection?

Accepted Answer

$$	heta_r = 	heta_i$$

Question 6

A planet orbits a star of mass $$M at $$radius $$r. $$According to Kepler’s third law, what is the orbital period $$T$$?

Accepted Answer

$$T^2$$ = \left(\frac{4\$$pi^2$$}{GM}\right) $$r^3$$

Question 7

A string of length $$L$$ and mass $$m is $$under tension $$T_s. $$What is the speed of a wave on the string?

Accepted Answer

$$v = \sqrt{\frac{T_s}{\mu}}$$

Question 8

A thin rod of mass $$M$$ and length $$L$$ rotates about its end. What is its moment of inertia?

Accepted Answer

$$I = \frac{1}{3}ML^2$

Question 9

A sound wave travels through water ($$B = 2.18 	imes 10^9$\ 	ext{Pa}$$, $$ho = 1000\ 	ext{kg/m}^3). $$What is the speed of sound in water?

Accepted Answer

$$v = \sqrt{\frac{B}{\rho}}$$

Question 10

A light ray in water ($$n = 1.33) $$strikes the water-air interface at $$60^\circ to $$the normal. Will total internal reflection occur?

Accepted Answer

Yes, because $$\sin 	heta_c = \frac{n_2$}{n_1$}$$ and $$	heta_i \u003e 	heta_c$$

Question 11

A double-slit experiment uses slits separated by $$d = 0.5\ 	ext{mm}$$ and a screen $$L = 2\ 	ext{m}$$ away. What is the distance between adjacent bright fringes for light of $$\lambda = 600\ 	ext{nm}$$?

Accepted Answer

$$y_m = \frac{\lambda L}{d}$$

Question 12

A thin lens creates a real image on the opposite side from the object. What is the sign of $$s'$$ according to the sign convention?

Accepted Answer

Positive

Question 13

A pendulum of length $$L$$ swings with small amplitude. What is its angular frequency?

Accepted Answer

$$\omega = \sqrt{\frac{g}{L}}$$

Question 14

A mass $$m$$ attached to a spring with constant $$k$$ oscillates. What is the equation for its displacement as a function of time?

Accepted Answer

$$x(t) = A \cos(\omega t + \$$phi_0$$)$$

Question 15

A wave on a string is described by $$D(x,t) = A \sin(kx - \omega t + \$$phi_0$$). $$What is the wavelength?

Accepted Answer

$$\lambda = \frac{2\pi}{k}$$

Question 16

A planet of mass $$m is at $$distance $$r$$ from a star of mass $$M. $$What is its gravitational potential energy?

Accepted Answer

$$U(r) = -\frac{GMm}{r}$$

Question 17

A cylindrical hoop of mass $$M$$ and radius $$R$$ rotates about its center. What is its moment of inertia?

Accepted Answer

$$I = MR^2$

Question 18

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

Accepted Answer

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

Comprehensive Study Guide for General Physics with Calculus (Ph212) – Final Exam Preparation

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