Q: A converging lens with focal length $$f = 10\ \mathrm{cm} is $$placed at the origin. An object is located $$30\ \mathrm{cm} to $$the left of the lens. What is the position of the image formed by the lens?

$$x = 15\ \mathrm{cm}$$\ \text{to the right of the lens}

Q: A thin film of oil ($$n = 1.40) $$floats on water ($$n = 1.33). $$For which minimum nonzero thickness will the film appear dark in reflected light of wavelength $$560\ \mathrm{nm} in $$air?

$$t = \dfrac{560\ \mathrm{nm}}{4 \times 1.40}$$

Q: In a double-slit experiment, the distance between the slits is $$d$$ and the screen is a distance $$L$$ away. For light of wavelength $$\lambda$$, what is the angular position $$\theta of $$the first-order bright fringe?

$$\sin\theta = \dfrac{\lambda}{d}$$

Q: A ray of light passes from glass ($$n=1.50) $$into water ($$n=1.33) at an $$angle of incidence of $$60^\circ. $$What is the critical angle for total internal reflection at this interface?

$$\theta_c = \arcsin\left(\dfrac{1.33}{1.50}\right)$$

Question 1

A converging lens with focal length $$f = 10\ \mathrm{cm} is $$placed at the origin. An object is located $$30\ \mathrm{cm} to $$the left of the lens. What is the position of the image formed by the lens?

Accepted Answer

$$x = 15\ \mathrm{cm}$$\ 	ext{to the right of the lens}

Question 2

A thin film of oil ($$n = 1.40) $$floats on water ($$n = 1.33). $$For which minimum nonzero thickness will the film appear dark in reflected light of wavelength $$560\ \mathrm{nm} in $$air?

Accepted Answer

$$t = \dfrac{560\ \mathrm{nm}}{4 	imes 1.40}$$

Question 3

A resistor of $$10\ \Omega is $$connected in series with a $$20\ \Omega$$ resistor and a $$12\ \mathrm{V}$$ battery. What is the current through the circuit?

Accepted Answer

$$I = 0.4\ \mathrm{A}$$

Question 4

Which of the following best describes the phenomenon of total internal reflection (TIR)?

Accepted Answer

Light is completely reflected back into the original medium when the angle of incidence exceeds the critical angle.

Question 5

A sound wave travels through air and encounters a wall. Which of the following statements is correct regarding the reflection of the wave?

Accepted Answer

The reflected wave may be inverted or upright depending on the boundary conditions.

Question 6

A parallel-plate capacitor is charged to a voltage $$V$$ and then disconnected from the battery. If the plate separation is doubled, what happens to the voltage across the plates?

Accepted Answer

The voltage doubles.

Question 7

A coil with $$N = 100$$ turns and area $$A = 0.01\ \mathrm{m}^2 is $$placed in a uniform magnetic field that increases from $$0 to$$ $$0.5\ \mathrm{T} in$$ $$0.1\ \mathrm{s}. $$What is the average induced emf in the coil?

Accepted Answer

$$\mathcal{E} = 10\ \mathrm{V}$$

Question 8

Which of the following is true about the image formed by a convex mirror?

Accepted Answer

The image is always virtual and upright.

Question 9

A string is fixed at both ends and vibrates at its fundamental frequency. If the length of the string is $$L$$ and the speed of the wave is $$v$$, what is the fundamental frequency?

Accepted Answer

$$f_1$$ = \dfrac{v}{2L}$$

Question 10

In a double-slit experiment, the distance between the slits is $$d$$ and the screen is a distance $$L$$ away. For light of wavelength $$\lambda$$, what is the angular position $$	heta of $$the first-order bright fringe?

Accepted Answer

$$\sin	heta = \dfrac{\lambda}{d}$$

Question 11

A ray of light passes from air ($$n=1.00) $$into glass ($$n=1.50) at an $$angle of incidence $$30^\circ. $$What is the angle of refraction in the glass?

Accepted Answer

$$19.5^\circ$$

Question 12

Which of the following best describes the relationship between electric field $$E$$, voltage $$V$$, and distance $$d in a $$uniform field?

Accepted Answer

$$E = \dfrac{V}{d}$$

Question 13

A wave pulse on a string reflects from a fixed end. What happens to the pulse upon reflection?

Accepted Answer

It is reflected inverted.

Question 14

A circuit contains a $$5\ \Omega$$ resistor and a $$10\ \Omega$$ resistor in parallel. What is the equivalent resistance?

Accepted Answer

$$R_{eq} = 3.33\ \Omega$$

Question 15

A traveling electromagnetic wave in the $$+x$$ direction has electric field amplitude $$E_{max}$$, period $$T$$, and wavelength $$\lambda. $$Which is a correct expression for the electric field as a function of $$x$$ and $$t ($$with $$\phi=0$$)?

Accepted Answer

$$E(x,t) = E_{max} \cos\left(2\pi\left(\dfrac{t}{T} - \dfrac{x}{\lambda}\right)\right)$$

Question 16

A tube open at both ends has a length $$L = 1.0\ \mathrm{m}. $$What is the fundamental frequency if the speed of sound is $$v = 340\ \mathrm{m/s}$$?

Accepted Answer

$$f_1 = 170$$\ \mathrm{Hz}$$

Question 17

Which of the following is a correct statement about the relationship between resistance $$R$$, resistivity $$\rho$$, length $$L$$, and area $$A of a $$wire?

Accepted Answer

$$R = \dfrac{\rho L}{A}$$

Question 18

In a double-slit experiment, what happens to the fringe spacing if the wavelength of light is doubled?

Accepted Answer

The fringe spacing is doubled.

Question 19

A ray of light passes from glass ($$n=1.50) $$into water ($$n=1.33) at an $$angle of incidence of $$60^\circ. $$What is the critical angle for total internal reflection at this interface?

Accepted Answer

$$	heta_c = \arcsin\left(\dfrac{1.33}{1.50}ight)$$

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