Conceptual Physics

sufficient angle of incidence, the angle of refraction reaches 90°, perpendicular to the

normal and parallel to the surface of the water. The light no longer crosses the interface

but remains in the water. The minimum angle of incidence at which this occurs is called

the critical angle.

Even at angles of incidence less than the critical angle there is some internal reflection

along with refraction. But when the critical angle is exceeded, there is no refraction at

all: All of the light is internally reflected.

Total internal reflection is shown in Concept 1. All the light is reflected back into the

water. Concept 2 shows the situation when the angle of incidence is equal to the critical

angle. The critical angle depends on the ratio of the indices of refraction of the two

media. You see this as the equation on the right, which is obtained by setting șr = 90º

(sosin șr = 1) in Snell’s law.

Diamonds rely on total internal reflection to achieve their sparkle. They are cut so that

light entering them reflects internally and emerges only at certain points, giving the

effect of scintillating light.

If you happen to have a diamond ring handy, you can demonstrate this dependence on

the ratio of indices by placing the ring in water. The sparkle disappears; this is because

the indices of refraction of diamond and water do not differ as significantly as those of

diamond and air, so the geometry of the ring no longer causes the same internal

reflection.

Engineers use total internal reflection in many different applications. For instance, right

isosceles prisms are used in binoculars to redirect light, as in the illustration below.

Fiber optic cable is used to transfer information (in glass or plastic) using total internal

reflection. Data (such as speech) is first encoded as modulations of a beam of laser

light. The light remains inside the transparent cable as it travels due to its total internal

reflection off the inner surfaces of the cable walls. In this way, light is transmitted

through the cable with little loss.

Using light instead of electricity to transfer information has several benefits. Light can be

used to encode much more information than electric oscillations because of its

extremely high frequency (more than 10^14 Hz for red light), and fiber optic cable is

immune to interference problems from nearby electrical applications.

Critical angle

Minimum incident angle for total internal

reflection

șc = critical angle

n 1 ,n 2 = indices of refraction (n 1 > n 2 )

You are cutting a sapphire to

make it as brilliant as possible.

Find the critical angle for the

sapphire in air. The index of

refraction of a sapphire is 1.77.

(^602) Copyright 2007 Kinetic Books Co. Chapter 32