Page 397 - Schaum's Outline of Theory and Problems of Applied Physics

382 LIGHT [CHAP. 30

As Fig. 30-11 shows, the angle of incidence must be 45 , so the critical angle must be at least 45 . Hence the
◦
◦
minimum value of n is
1 1
n = = = 1.41
sin i c sin 45 ◦

45°
45°

Fig. 30-11

APPARENT DEPTH
An object submerged in water or other transparent liquid appears closer to the surface than it actually is. As
Fig. 30-12 shows, light leaving the object is bent away from the normal to the water-air surface as it leaves the
water. Since an observer interprets what she or he sees in terms of the straightline propagation of light, the object
seems at a shallower depth than its true one. The ratio between apparent and true depths is

Apparent depth h n 2
= =
True depth h n 1
where n 1 is the index of refraction of the liquid and n 2 is the index of refraction of air.

h′ = apparent depth

h = true depth

Fig. 30-12

SOLVED PROBLEM 30.20
The water in a swimming pool is 2 m deep. How deep does it appear to be to someone looking down
into it?
Here n 1 = 1.33 and n 2 = 1.00, so

n 2 1.00
h = h = (2m) = 1.5m

n 1 1.33
Multiple-Choice Questions

30.1. The magnetic field of an electromagnetic wave is
(a) parallel to the electric field and to the wave direction
(b) parallel to the electric field and perpendicular to the wave direction
(c) perpendicular to the electric field and to the wave direction
(d) perpendicular to the electric field and parallel to the wave direction