Q: What is the critical angle for total internal reflection for light traveling from glass ($$n = 1.50) $$into air ($$n = 1.00$$)?

$$\theta_c = \arcsin\left(\frac{n_2$}{n_1$}\right) = \arcsin\left(\frac{1.00}{1.50}\right) \approx 41.8^\circ$$

Q: A ray of light is incident at Brewster’s angle on a glass surface ($$n = 1.50). $$What is the value of Brewster’s angle?

$$\theta_B = \arctan\left(\frac{n_2$}{n_1$}\right) = \arctan\left(\frac{1.50}{1.00}\right) \approx 56.3^\circ$$

Question 1

A ray of light strikes a plane mirror at an angle of $$30^\circ$$ with respect to the normal. What is the angle between the incident ray and the reflected ray?

Accepted Answer

$$60^\circ$$

Question 2

Which of the following statements about images formed by plane mirrors is correct?

Accepted Answer

The image is upright and appears the same distance behind the mirror as the object is in front.

Question 3

A concave spherical mirror has a radius of curvature $$R = 40\ \mathrm{cm}. $$What is its focal length?

Accepted Answer

$$f = 20\ \mathrm{cm}$$

Question 4

Which of the following best describes spherical aberration in mirrors?

Accepted Answer

It occurs when rays far from the principal axis do not converge at a single focal point.

Question 5

A real object is placed $$30\ \mathrm{cm} in $$front of a concave mirror with a focal length of $$10\ \mathrm{cm}. $$Where is the image formed?

Accepted Answer

$$\displaystyle \frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i} \Rightarrow d_i = 15\ \mathrm{cm} (on $$the same side as the object)

Question 6

Which of the following is true for the sign conventions of the mirror equation?

Accepted Answer

The image distance is positive for real images.

Question 7

A light ray passes from air ($$n = 1.00) $$into water ($$n = 1.33) at an $$angle of $$45^\circ to $$the normal. What is the angle of refraction in the water?

Accepted Answer

$$n_1$$ \sin \$$theta_1$$ = $$n_2$$ \sin \$$theta_2$$ \Rightarrow \$$theta_2$$ \approx 32^\circ$$

Question 8

Which phenomenon explains why a straw appears bent when placed in a glass of water?

Accepted Answer

Refraction

Question 9

What is the critical angle for total internal reflection for light traveling from glass ($$n = 1.50) $$into air ($$n = 1.00$$)?

Accepted Answer

$$	heta_c = \arcsin\left(\frac{n_2$}{n_1$}ight) = \arcsin\left(\frac{1.00}{1.50}ight) \approx 41.8^\circ$$

Question 10

A double convex lens has a focal length of $$20\ \mathrm{cm}. An $$object is placed $$30\ \mathrm{cm}$$ from the lens. Where is the image formed?

Accepted Answer

$$\displaystyle \frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i} \Rightarrow d_i = 60\ \mathrm{cm}$$

Question 11

Which of the following best describes the effect of dispersion in a prism?

Accepted Answer

Higher frequency light is refracted more than lower frequency light.

Question 12

A ray of light is incident at Brewster’s angle on a glass surface ($$n = 1.50). $$What is the value of Brewster’s angle?

Accepted Answer

$$	heta_B = \arctan\left(\frac{n_2$}{n_1$}ight) = \arctan\left(\frac{1.50}{1.00}ight) \approx 56.3^\circ$$

Question 13

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

Accepted Answer

The image is upright and smaller than the object.

Question 14

A lens forms an image with a magnification $$m = -2. $$Which of the following is true?

Accepted Answer

The image is inverted and twice as large as the object.

Question 15

Which of the following best explains why rainbows form after a rainstorm?

Accepted Answer

Dispersion of sunlight as it refracts and reflects inside raindrops.

Question 16

A diverging lens has a focal length of $$-15\ \mathrm{cm}. An $$object is placed $$10\ \mathrm{cm}$$ from the lens. What is the image distance?

Accepted Answer

$$\displaystyle \frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i} \Rightarrow d_i = -6\ \mathrm{cm}$$

Question 17

Which of the following statements about the thin-lens equation is correct?

Accepted Answer

It relates the object distance, image distance, and focal length of a lens.

Geometrical Optics: Study Notes for Physics with Calculus

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