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TUTORIAL SHEET 1
1. If Dotto’s face is 30.0 cm in front of a concave shaving mirror creating an upright image 1.50
times as large as the object, what is the mirror’s focal length?
2. A Material Science and Solar Energy group of the University of Dar es Salaam is planning
to construct a solar cooker by using a concave mirror to reflect and focus sunlight into a
cooking vessel. As an expert, what advice would you provide to them during design of the
reflecting mirror that would guarantee very high temperatures?
3. Determine the minimum height of a vertical flat mirror in which Ms Pendo who is 178 cm tall
can see her full image.
4. An object is placed 50.0 cm from a concave spherical mirror with focal length of magnitude
20.0 cm. (a) Find the location of the image. (b) What is the magnification of the image? (c) Is
the image real or virtual? (d) Is the image upright or inverted?
5. A concave spherical mirror has a radius of curvature of magnitude 20.0 cm. (a) Find the
location of the image for object distances of (i) 40.0 cm, (ii) 20.0 cm, and (iii) 10.0 cm. For
each case, state whether the image is (b) real or virtual and (c) upright or inverted. (d) Find the
magnification in each case.
6. A convex spherical mirror has a radius of curvature of magnitude 40.0 cm. Determine the
position of the virtual image and the magnification for object distances of (a) 30.0 cm and (b)
60.0 cm. (c) Are the images in parts (a) and (b) upright or inverted?
7. An object of height 2.00 cm is placed 30.0 cm from a convex spherical mirror of focal length
of magnitude 10.0 cm. (a) Find the location of the image. (b) Indicate whether the image is
upright or inverted. (c) Determine the height of the image.
8. Dr Yekonia uses a spherical mirror to examine the tooth of a patient. The tooth is 1.00 cm in
front of the mirror, and the image is formed 10.0 cm behind the mirror. Determine (a) the
mirror’s radius of curvature and (b) the magnification of the image.
9. (a) A concave spherical mirror forms an inverted image 4.00 times larger than the object.
Assuming the distance between object and image is 0.600 m, find the focal length of the mirror.
(b) What If? Suppose the mirror is convex. The distance between the image and the object is
the same as in part (a), but the image is 0.500 the size of the object. Determine the focal length
of the mirror.
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10. (a) A concave spherical mirror forms an inverted image different in size from the object by a
factor a > 1. The distance between object and image is d. Find the focal length of the mirror.
(b) What If? Suppose the mirror is convex, an upright image is formed, and a < 1. Determine
the focal length of the mirror.
11. Figure 1 shows a curved surface separating a material with index of refraction 1 from a
material with index 2. The surface forms an image I of object O. The ray shown in red passes
through the surface along a radial line. Its angles of incidence and refraction are both zero, so
its direction does not change at the surface. For the ray shown in blue, the direction changes
according to Snell’s law, 1sin1 = 2sin2. For paraxial rays, we assume 1 and 2 are small,
so we may write 1tan1 = 2tan2. The magnification is defined as M = h’/h. Prove that the
magnification is given by M = -1q/2p.
Figure 1
12. The top of a swimming pool is at ground level. If the pool is 2.00 m deep, how far below
ground level does the bottom of the pool appear to be located when (a) the pool is completely
filled with water? (b) When it is filled halfway with water?
13. The wavelength of red helium–neon laser light in air is 632.8 nm. (a) What is its frequency?
(b) What is its wavelength in glass that has an index of refraction of 1.50? (c) What is its speed
in the glass?
14. A ray of light is incident on a flat surface of a block of crown glass that is surrounded by water.
The angle of refraction is 19.6°. Find the angle of reflection.
15. A light ray initially in water enters a transparent substance at an angle of incidence of 37°, and
the transmitted ray is refracted at an angle of 25°. Calculate the speed of light in the transparent
substance.
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16. A light beam containing red and violet wavelengths is incident on a slab of quartz at an angle
of incidence of 50°. The index of refraction of quartz is 1.455 at 600 nm (red light), and its
index of refraction is 1.468 at 410 nm (violet light). Find the dispersion of the slab, which is
defined as the difference in the angles of refraction for the two wavelengths.
17. A glass optical fiber (n = 1.50) is submerged in water (n = 1.33). What is the critical angle for
light to stay inside the fiber?
18. A beam of light is incident from air on the surface of a liquid. If the angle of incidence is 30°
and the angle of refraction is 22°, find the critical angle for total internal reflection for the
liquid when surrounded by air.
19. A light ray traveling in air is incident on one face of a right-angle prism with index of refraction
n = 1.50 as shown in Figure 2, and the ray follows the path shown in the figure. Assuming 
= 60° and the base of the prism is mirrored, determine the angle  made by the outgoing ray
with the normal to the right face of the prism.
20. A ray of light passes from air into water. For its deviation angle  = |1 -2| to be 10°, what
must its angle of incidence be?
Figure 2