Q: A swimmer underwater (water $$n=1.33) $$looks up at the water-air interface. What is the critical angle for total internal reflection?

$$\theta_c = \arcsin\left(\frac{n_2$}{n_1$}\right) = \arcsin\left(\frac{1.00}{1.33}\right) \approx 48.7^\circ$$

Question 1

Which of the following statements best describes the ray model of light?

Accepted Answer

Light rays travel in straight lines and cross without interacting unless they encounter matter.

Question 2

A camera obscura forms an image of a tree on its back wall. If the object distance is $$d_o$$ and the image distance is $$d_i$$, and the object height is $$h_o$$, what is the formula for the image height $$h_i$$?

Accepted Answer

$$h_i = \frac{d_i}{d_o} h_o$$

Question 3

Which of the following is an example of a self-luminous object?

Accepted Answer

The Sun

Question 4

What is the law of reflection for a light ray incident on a flat mirror?

Accepted Answer

$$	heta_r = 	heta_i$$

Question 5

A light ray in air ($$n_1 = 1.00$) strikes a glass surface (n_2$ = 1.50) at an $$angle of $$30^\circ$$ from the normal. What is the angle of refraction in the glass?

Accepted Answer

$$\$$theta_2$$ = \arcsin\left(\frac{n_1$}{n_2$} \sin \$$theta_1$$\right) = \arcsin\left(\frac{1.00}{1.50} \sin 30^\circ\right) \approx 19.5^\circ$$

Question 6

A swimmer underwater (water $$n=1.33) $$looks up at the water-air interface. What is the critical angle for total internal reflection?

Accepted Answer

$$	heta_c = \arcsin\left(\frac{n_2$}{n_1$}ight) = \arcsin\left(\frac{1.00}{1.33}ight) \approx 48.7^\circ$$

Question 7

A 3.0-cm-high object is placed 20 cm in front of a concave mirror with a radius of curvature of 80 cm. Where is the image formed and what is its magnification?

Accepted Answer

The image is 40 cm behind the mirror, virtual, and magnified by $$m = +2.0.$$

Question 8

A biologist uses a magnifying lens 2.0 cm above a specimen and observes a magnification of 4.0. What is the focal length of the lens?

Accepted Answer

$$f = 2.7\ \mathrm{cm}$$

Question 9

Which of the following best describes the difference between specular and diffuse reflection?

Accepted Answer

Specular reflection occurs on smooth surfaces and produces parallel reflected rays; diffuse reflection occurs on rough surfaces and scatters rays in many directions.

Question 10

A goldfish is 10 cm from the inner surface of a spherical fish bowl (diameter 50 cm, $$n_{water}=1.33). $$Where does the fish appear to an observer outside the bowl (in air, $$n=1.00$$)?

Accepted Answer

The fish appears to be 8.3 cm from the surface.

Question 11

A diverging lens with focal length $$f = -50 cm is $$placed 100 cm from a flower. Where is the image and what is its magnification?

Accepted Answer

The image is 33 cm to the left of the lens, virtual, with $$m = +0.33.$$

Question 12

Which equation correctly relates the object distance $$s$$, image distance $$s'$$, and focal length $$f$$ for a thin lens?

Accepted Answer

$$\frac{1}{s} + \frac{1}{s'} = \frac{1}{f}$$

Question 13

A light ray passes from glass ($$n=1.50) $$into air ($$n=1.00). $$What happens if the angle of incidence exceeds the critical angle?

Accepted Answer

Total internal reflection occurs and all the light is reflected back into the glass.

Question 14

Which of the following is the correct lens maker's equation for a lens in air?

Accepted Answer

$$\frac{1}{f} = (n-1) \left( \frac{1}{R_1$} - \frac{1}{R_2$} \right)$$

Question 15

A fiber optic cable uses total internal reflection to transmit light. Which condition must be satisfied for TIR to occur inside the fiber?

Accepted Answer

The core must have a higher index of refraction than the cladding ($$n_{core} \u003e n_{cladding}).$$

Question 16

A converging lens forms a real image of an object placed outside its focal length. Which statement is true about the image?

Accepted Answer

The image is inverted and can be projected onto a screen.

Question 17

Which of the following best describes the formation of a virtual image by a plane mirror?

Accepted Answer

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

Ray Optics and Image Formation: Study Notes

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