Q: A swimmer underwater looks up at the surface and sees a bright circle above. This phenomenon is due to total internal reflection. If the water has an index of refraction $$n_1 = 1.33$ and air has n_2$ = 1.00$$, what is the critical angle for total internal reflection at the water-air interface?

$$\theta_c = \arcsin\left(\frac{n_2$}{n_1$}\right) = \arcsin\left(\frac{1.00}{1.33}\right) \approx 48.8^\circ$$

Q: A rodent 0.20 m tall stands 0.3 m from a biconcave lens with a focal length of $$-0.60 m. $$What is the height of the image?

The image height is $$h_i = h_o \cdot \left|\frac{d_i}{d_o}\right| = 0.20 \times \frac{0.2}{0.3} = 0.13 m$$, upright and reduced.

Q: A light ray passes from water ($$n=1.33) $$into air ($$n=1.00) at an $$incident angle of $$60^\circ. $$Will total internal reflection occur?

Yes, because $$60^\circ \u003e \theta_c$$ for the water-air interface.

Question 1

A duck is swimming on a calm lake and you see its reflection clearly, as shown in the image. What type of image is formed by the water surface, and what are its properties?

Accepted Answer

A virtual, upright, and same-size image

Question 2

A laser beam strikes a plane mirror at an angle of incidence of $$30^\circ. $$What is the angle between the incident and reflected rays?

Accepted Answer

$$60^\circ$$

Question 3

A swimmer underwater looks up at the surface and sees a bright circle above. This phenomenon is due to total internal reflection. If the water has an index of refraction $$n_1 = 1.33$ and air has n_2$ = 1.00$$, what is the critical angle for total internal reflection at the water-air interface?

Accepted Answer

$$	heta_c = \arcsin\left(\frac{n_2$}{n_1$}ight) = \arcsin\left(\frac{1.00}{1.33}ight) \approx 48.8^\circ$$

Question 4

A 1.60 m tall woman stands in front of a vertical plane mirror. What is the minimum length of the mirror required for her to see her entire body?

Accepted Answer

0.80 m

Question 5

A beam of light passes from air ($$n=1.00) $$into glass ($$n=1.50) at an $$incident angle of $$35^\circ. $$What is the angle of refraction in the glass?

Accepted Answer

$$\sin$$^{-1}$$\left(\frac{1.00}{1.50} \sin 35^\circ\right) \approx 22.3^\circ$$

Question 6

A solar cooker uses a concave mirror to focus sunlight. If the focal length of the mirror is 18.0 cm, what is the radius of curvature of the mirror?

Accepted Answer

$$r = 2f = 36.0\ 	ext{cm}$$

Question 7

A stamp collector uses a converging lens with a focal length of 20 cm to view a stamp 15 cm in front of the lens. Using the thin lens equation, where is the image formed?

Accepted Answer

$$\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i} \Rightarrow d_i = \left(\frac{1}{20\ 	ext{cm}} - \frac{1}{15\ 	ext{cm}}\$$right)^{-1}$$ = -60\ 	ext{cm} ($$virtual, on the same side as the object)

Question 8

A rodent 0.20 m tall stands 0.3 m from a biconcave lens with a focal length of $$-0.60 m. $$What is the height of the image?

Accepted Answer

The image height is $$h_i = h_o \cdot \left|\frac{d_i}{d_o}ight| = 0.20 	imes \frac{0.2}{0.3} = 0.13 m$$, upright and reduced.

Question 9

A light ray passes from water ($$n=1.33) $$into air ($$n=1.00) at an $$incident angle of $$60^\circ. $$Will total internal reflection occur?

Accepted Answer

Yes, because $$60^\circ \u003e 	heta_c$$ for the water-air interface.

Question 10

A prism splits white light into a spectrum of colors. What is the physical reason for this phenomenon?

Accepted Answer

Different wavelengths of light have different indices of refraction in the prism material (dispersion).

Question 11

A person wants to shoot a fish underwater with a spear gun. Should they aim directly at the image, slightly above, or slightly below the apparent position of the fish?

Accepted Answer

Aim slightly below the image.

Question 12

A fiber optic cable uses total internal reflection to transmit light. Which of the following must be true for total internal reflection to occur inside the fiber?

Accepted Answer

The core must have a higher index of refraction than the cladding.

Question 13

A child uses a magnifying glass (converging lens) with a focal length of 6.0 cm to view a flower 4.0 cm from the lens. What is the magnification?

Accepted Answer

$$M = -\frac{d_i}{d_o}$$, where $$d_i = \left(\frac{1}{6.0} - \frac{1}{4.0}\$$right)^{-1}$$ = -12 cm$$, so $$M = -\frac{-12}{4} = 3 ($$upright, enlarged)

Question 14

A convex mirror has a radius of curvature $$R = 10 cm. $$What is its focal length?

Accepted Answer

$$f = -\frac{R}{2} = -5 cm$$

Question 15

A person looks at their reflection in a shiny Christmas ornament (convex mirror) with a diameter of 10 cm. If their face is 30 cm away from the ornament, where is the image formed?

Accepted Answer

The image is formed at $$d_i = \left(\frac{1}{f} - \frac{1}{d_o}\$$right)^{-1}$$, with f = -5$ cm, d_o = 30$ cm, so d_i$$ \approx -4.3$$ cm (virtual, behind the mirror).

Question 16

Which of the following best explains why car headlights appear dimmer on a rainy day?

Accepted Answer

Raindrops create a rough surface, causing diffuse reflection and scattering light in many directions.

Question 17

A lightbulb is set at the bottom of a 3.0-m-deep swimming pool. What is the diameter of the circle inside which a duck swimming on the surface could see the bulb? (Use $$n_{water} = 1.33$$, $$n_{air} = 1.00.)$$

Accepted Answer

$$D = 2h 	an 	heta_c$$, where $$	heta_c = \arcsin\left(\frac{1.00}{1.33}ight) \approx 48.8^\circ$$, so $$D = 2 	imes 3.0 	imes 	an 48.8^\circ \approx 6.8 m$$

Ray Optics: Mirrors, Lenses, and Image Formation

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