Reflection (continuation)

The figure 3 below shows rays from a point source in glass falling on a glass-air interface. As the angle of incidence q is increased, we reach a situation (see ray e) at which the refracted ray points along the surface, the angle of refraction being 90°. For angles of incidence larger than this critical angle q_c, there is no refracted ray and we talk about total internal reflection.

We find the critical angle by putting q₂ =90° in the law of refraction:

 n₁sin=q_c =n₂sin90°,

Or

 q_c =sin^-1(n₂/n₁)

For glass in air, q_c=sin^-1(1.00/1.50)=41.8°. Figure 5 indicates that the energy of the reflected wave becomes 100% when the angle of incidence exceeds 41.8°.

FIGURE 5 Credits: Halliday David

The sine of an angle cannot exceed unity so that we must have n₂ <n_1. This means that total internal reflection cannot occur when the incident light is in the medium of lower index of refraction. The word total means just that, the reflection occurs with no loss of intensity. In ordinary reflection from a mirror, by way of contrast, there is an intensity loss of about 4%.

FIGURE 21 Credits: Halliday David

Total internal reflection makes possible fiber optical devices by means which physicians can visually inspect many internal body sites.In these devices, a bundle of fibers transmits an image that can be inspected visually outside the body. Optical fibers are also used for telephone communications and because of their light weight and freedom from electromagnetic interference, for carrying signals on aircraft. Figure 21 shows light emerging from an optical fiber.

FIGURE 22 Credits: Halliday David

As Figure 22 shows, the fiber consists of a central core that is graded smoothly into an outer cladding layer if material of lower index of refraction. Only those rays that are internally reflected can be propagated along the fiber. To reduce attenuation of the signal as it passes along the fiber, materials of extreme purity have been developed. If seawater were as transparent as the glass from which optical fibers are made, it would be possible to see the sea bottom by reflected sunlight at a depth of several miles.