Refraction unit worksheet
Learning Goals
I can calculate the angle of refraction
I can do calculations and draw accurate ray diagrams for lenses
1. A ray of light of vacuum wavelength 550 nm traveling in air enters a slab of transparent material. The
incoming ray makes an angle of 40º with the normal, and the refracted ray makes an angle of 26º with
the normal. Find the index if refraction of the transparent material. (Assume that the index of
refraction of air for light of wavelength 550 nm is 1.00.) (nr = 1.466)
2. Find the angle of refraction of a ray of light that enters a diamond from air at an angle of 15º to the
normal. For diamond, n = 2.419 and for air, n = 1.000. (θr = 6.14o)
3. Light passes from air into water at an angle of incidence of 42.3º. Determine the angle of refraction
in the water (n = 1.333). (θr = 30.32o)
4. A ray of light enters the top of a glass of water (n = 1.333) at an angle of 36º with the vertical. What
is the angle between the refracted ray and the vertical? (θr = 26.17o)
5. A narrow ray of yellow light from glowing sodium (λ0 = 589 nm) traveling in air strikes a smooth
surface of water (n = 1.333) at an angle of θi = 35º. What is the angle of refraction, θr? (θr = 25.49o)
6. A ray of light traveling in air strikes a flat 2.00 cm thick block of glass (n = 1.50) at an angle of 30º with
the normal. Trace the light ray through the glass, and find the angles of incidence and refraction at each
surface. (This includes the ray exiting the block of glass.) (θr = 19.47o, θr = 30o)
7. The light ray shown in Figure 15-18 makes an angle of 20º with the normal line at the boundary of
linseed oil and water. Determine the angles θ1 and θ2. Note that n = 1.48 for linseed oil. (θ1 = 30.41o, θ2
= 22.32o)
8. Calculate the critical angle for light traveling from glycerine (n = 1.473) into water (n = 1.333). (θc =
64.82o)
9. Find the critical angle for light traveling from ice (n = 1.309) into air (n = 1.000). (θc = 49.81o)
10. Which has a smaller critical angle in air, diamond (n = 2.419) or cubic zirconia (n = 2.20)? (diamond)
11. Find the critical angle for light traveling from water into ice. (θc = 79.11o)
12. Calculate the critical angle for light going from glycerine into air. (θc = 42.76o)
13. Light traveling in air enters the flat side of a prism made of crown glass (n = 1.52), as shown in Figure
15-19. Will the light pass through the other side of the prism or will it be totally internally reflected?
Show your work. (total internally reflected)
14. Sherlock Holmes examines a clue by holding his magnifying glass (with a focal length of 15 cm) 10
cm away from an object. Find the image distance and the magnification. Describe the image that he
observes. (q = -30cm, M = 3)
15. An object is placed 20 cm in from of a diverging lens of focal length 10 cm. Find the image distance
and the magnification. Describe the image. (q = -6.67 cm, M = 0.333)
16. An object is placed in front of a diverging lens with a focal length of 20 cm. For each object distance,
find the image distance and the magnification. Describe each image.
a. 40 cm (q = -13.3 cm, M = 0.3)
b. 20 cm (q = -10 cm, M = 0.5)
c. 10 cm (q = -6.6 cm, M = 0.6)
17. A person looks at a gem using a converging lens with a focal length of 12.5 cm. The lens forms a
virtual image 30 cm from the lens. Determine the magnification. Is the image upright or inverted?
Draw a ray diagram to confirm your results. (p = 21.4 cm, M = -1.4)
18. An object is placed in front of a converging lens with a focal length of 20 cm. For each object
distance, find the image distance and the magnification. Describe each image with a ray diagram.
a. 40 cm (q = 40 cm, M = -1)
b. 10 cm (q = -20 cm, M = 2)
19. A magnifying glass has a converging lens of focal length 15 cm. At what distance from a nickel
should you hold this lens to get an image with a magnification of + 2.00? (p = 7.5 cm)
20. Where must an object be placed to have a magnification of 2.00 in each of the following cases?
Show your work.
a. a converging lens of focal length 12 cm (p = 6 cm)
b. a diverging lens of focal length 12 cm (p = 0 cm)