Total internal reflection and critical angle

When light passes from a material such as water into one of lower refractive index such as air it is found that there is a maximum angle of incidence in the water that will give a refracted beam in the air, that is, the angle of refraction is 90^o. The angle of incidence in the denser medium corresponding to an angle of refraction of 90^o in the less dense medium is known as the critical angle (c) (Figure 1). The reason for this is clear if we consider the formulae. For an angle of refraction of 90^o we have:

₂n₁= sin i/ sin r = sin c/ sin 90 = 1/₁n₂
For light passing from a material of absolute refractive index n₁ to one of absolute refractive index n₂ we have:

For an air-glass boundary, with n = 1.5, c = 42^o and for an air-water boundary c = 48.5^o.

For angles of incidence greater than the critical angle all the light is reflected back into the optically more dense material, that is, the one with the greater refractive index. This is known as total internal reflection and the normal laws of reflection are obeyed.

Total internal reflection explains the shiny appearance of the water surface of a swimming pool when viewed at an angle from below. The phenomenon is used in prismatic binoculars. (See: Prisms)

(Mirages are caused by continuous internal reflection. (See: Mirages)

It is left as an exercise for you to prove that light cannot pass across the corner of a right-angled glass block if the refractive index of the glass is 1.5 (see Figure 2).

This inability of light to pass across the corner of a right-angled glass block when the block is in air is used in the depth gauge shown in Figure 3. In diagram (a) the rod is in air and so the light is reflected back to the top. In diagram (b) the rod is in water which has a refractive index (1.33) closer to that of glass. This will increase the critical angle and so light can escape in to the water across the right angle.

The two photographs show this effect when attempting to look across the corner of a right-angled fish tank.

schoolphysics: Total internal reflection animation

To see an animation of total internal reflection click on the animation link.

schoolphysics: Total internal reflection simulated experiment animation

To carry out an interactive experiment on total internal reflection click on the animation link.