Solutions to homework problem set #3
Text pages 69-71, problems P12, P19, P21, P23, PM2
P12. figures a and c are possible because it is possible to draw a ray from the object to the eye that reflects from the mirror and satisfies the requirement that the angle of incidence equals the angle of reflection. This is not possible for case b, since the eye is directly above the mirror and the object is too far to the right to satisfy the angle requirement.
P19. By cupping your hands around the side of your head you block the outside light that is reflected from the window. Even though the window reflects only 4% of the outside light, this reflection is generally brighter than the light transmitted from the inside, so that objects inside cannot be seen against this brighter reflection.
P21. The index of refraction increases with increasing frequency. Therefore, the index of refraction of blue light is larger than the index for red light. Since the velocity in the medium is c/n, a larger index means a smaller velocity, so that blue light has a smaller velocity in glass than red light. Thus the answer is (a) – red light travels faster than blue light in glass.
P23. When light is refracted from a medium with a higher index of refraction to a medium with a lower index of refraction (for example, from glass into air), the refracted light is bent away from the normal. When the incident angle is large enough, the refracted ray emerges at 90 degrees to the normal. The angle at which this happens is the critical angle – it is the incident angle at which the refracted ray first disappears.
(a) The index of refraction is the ratio of the speed of light in vacuum to the speed in the material. The index of refraction is therefore
300,000/200,000 = 1.5
(b) If the index of refraction of diamond is 2.5, the speed of light in this diamond is 300,000/2.5 = 120,000 km/s