Q: A beam of light in water ($$n_1 = 1.33$) strikes the water-air interface. What is the critical angle $$\theta_c$$ for total internal reflection?

$$\theta_c = \sin$$^{-1}$$\left(\frac{1.00}{1.33}\right) = 48.8^\circ$$

Q: A ray of light in glass ($$n = 1.5) $$strikes the glass-air interface at $$60^\circ to $$the normal. Will total internal reflection occur?

Yes, because $$\$$theta_1$$ \u003e \theta_c$$ where $$\theta_c = \sin$$^{-1}$$\left(\frac{1.00}{1.50}\right) = 41.8^\circ$$

Question 1

A light ray passes from air (n = 1.00) into glass (n = 1.50) at an angle of incidence $$\$$theta_1$$ = 30^\circ. $$What is the angle of refraction $$\$$theta_2$$ in the glass?

Accepted Answer

$$\$$theta_2$$ = \sin$$^{-1}$$\left(\frac{1.00}{1.50} \sin 30^\circ\right) = 19.5^\circ$$

Question 2

Which law governs the relationship between the angle of incidence and the angle of reflection for a light ray striking a surface?

Accepted Answer

Law of Reflection: $$\$$theta_1$$' = \$$theta_1$$

Question 3

A beam of light in water ($$n_1 = 1.33$) strikes the water-air interface. What is the critical angle $$	heta_c$$ for total internal reflection?

Accepted Answer

$$	heta_c = \sin$$^{-1}$$\left(\frac{1.00}{1.33}ight) = 48.8^\circ$$

Question 4

For a plane mirror, if an object is placed 25 cm in front of the mirror, where is the image located?

Accepted Answer

25 cm behind the mirror

Question 5

A concave mirror has a radius of curvature $$r = 40 cm. $$What is its focal length $$f$$?

Accepted Answer

$$f = \frac{1}{2} r = 20 cm$$

Question 6

An object is placed 10 cm in front of a converging lens with a focal length of 20 cm. Where is the image formed?

Accepted Answer

$$\frac{1}{p} + \frac{1}{i} = \frac{1}{f} \Rightarrow \frac{1}{10} + \frac{1}{i} = \frac{1}{20} \Rightarrow i = -20 cm ($$virtual, same side as object)

Question 7

A real image is formed by a lens only when:

Accepted Answer

The object is outside the focal point of a converging lens

Question 8

A lens has radii of curvature $$r_1 = +10$ cm and r_2$ = -10 cm$$, and refractive index $$n = 1.5. $$What is its focal length $$f in $$air?

Accepted Answer

$$\frac{1}{f} = (n-1)\left(\frac{1}{r_1$} - \frac{1}{r_2$}\right) = (0.5)\left(\frac{1}{10} + \frac{1}{10}\right) = 0.1 \Rightarrow f = 10 cm$$

Question 9

If the magnification $$m of a $$mirror is negative, what does this indicate about the image?

Accepted Answer

The image is inverted

Question 10

A ray of light in glass ($$n = 1.5) $$strikes the glass-air interface at $$60^\circ to $$the normal. Will total internal reflection occur?

Accepted Answer

Yes, because $$\$$theta_1$$ \u003e 	heta_c$$ where $$	heta_c = \sin$$^{-1}$$\left(\frac{1.00}{1.50}ight) = 41.8^\circ$$

Question 11

Which of the following best describes the image formed by a convex mirror for any object position?

Accepted Answer

Virtual, upright, and reduced in size

Question 12

A thin lens produces a magnification $$m = -2. $$What does this tell you about the image?

Accepted Answer

The image is real, inverted, and twice as large as the object

Question 13

A diverging lens always produces which type of image?

Accepted Answer

Virtual, upright, and reduced

Question 14

A 1 cm tall object is placed 15 cm in front of a concave mirror with a focal length of 10 cm. What is the image distance $$i$$?

Accepted Answer

$$\frac{1}{p} + \frac{1}{i} = \frac{1}{f} \Rightarrow \frac{1}{15} + \frac{1}{i} = \frac{1}{10} \Rightarrow i = 30 cm$$

Question 15

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

Accepted Answer

The image is virtual, upright, and the same size as the object

Question 16

A lens is made of glass ($$n = 1.6) $$with radii of curvature $$r_1 = +20$ cm and r_2$ = -20 cm. $$What is the focal length $$f$$?

Accepted Answer

$$\frac{1}{f} = (1.6-1)\left(\frac{1}{20} + \frac{1}{20}\right) = 0.06 \Rightarrow f = 16.7 cm$$

Question 17

If a ray of light passes from glass ($$n = 1.5) $$into water ($$n = 1.33$$), what happens to the ray?

Accepted Answer

It bends away from the normal

Question 18

A virtual image is always formed by which of the following?

Accepted Answer

A plane mirror

Question 19

A person uses a concave shaving mirror with a radius of curvature of 35 cm and sees an upright image 2.5 times the size of their face. How far is their face from the mirror?

Accepted Answer

$$p = \frac{r}{2(1-1/m)} = \frac{35}{2(1-1/2.5)} = 10.5 cm$$

Ray Optics: Reflection, Refraction, Mirrors, and Lenses

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