Chapter 26: Geometrical Optics
5. The image shows sunlight entering the room at an angle of 32,
reflecting off a horizontal mirror and shining on a wall 2.0 m
away. The image also shows the reflected ray after the mirror is
tilted by 5.0.
Calculate the initial height of the reflection by setting the tangent
of the 32° incoming angle equal to the height divided by the
distance from the wall. The reflected angle increases by twice the
angle of rotation when the mirror is tilted. Calculate the new height
using the tangent of the incoming angle plus twice the angle of
rotation. Subtract the two heights to calculate y.
1. Calculate the initial height of the reflection:
2.0 m tan 32
2. Calculate the final height after the rotation:
2.0 m tan 32 +10
3. Subtract the two heights:
1.80 m 1.25 m 0.55 m = 55 cm
7. The image shows you observing your belt buckle in a small vertical mirror
hanging on a wall 2.3 meters in front of you. The location of the mirror is a
distance h below your eye level.
the mirror must be midway between your eyes and belt
buckle. Calculate the angle of reflection (the angle you must look down to
see your belt buckle) from the inverse tangent of the ratio of the mirror
height and distance.
1. (a) Calculate the height of the mirror:
0.72 m 2
2. (b) Calculate the reflected angle:
1 0.36 m
3. (c) Because the vertical position of the mirror relative to your eyes is halfway between your eyes and belt buckle,
regardless of the distance you stand from the mirror, you will still see the buckle even if you move backward.
26. An object is placed in front of a concave mirror. The mirror
produces a real, magnified image.
Use equation 26-3 to calculate the focal length from the radius of
curvature. Then use equation 26-6 to calculate the image distance.