Total internal reflection occurs when:
The ray of light passes from a denser to a less dense medium;
The angle of incidence in the denser medium is greater than the critical angle.
The critical angle is defined as the angle of incidence in the optically dense medium for which the angle of refraction in the less dense medium is 90°. If the angle of incidence is greater than the critical angle than no refraction occurs. The light is strongly reflected, which is called total internal reflection.
A relationship between the critical angle and the refraction index can be drawn, when e.g. a light ray travels from a dense medium into a less dense medium, the angle of incidence i, becomes the critical angle c, so the angle of refraction r is 90° i.e. : i = c and r = 90°
Therefore, by the principle reversibility of light : n = sin 90°/ sin c = 1/sin c
Therefore, sin c = 1/n
Total internal reflection can be demonstrated using a semi-circular glass block and a ray box:
1) Place the semi-circular block in the middle of a sheet of white paper. Draw around the block to record its position. 2) Direct a ray of light at the curved surface of the block so that it passes straight in and reaches the midpoint of the flat side of the block.
3) Observe the refracted ray passing through the block. Observe also the reflected ray.
4) Mark two dots on the incident ray to record its position. Repeat with the reflected ray and the refracted ray. Remove the ray box and the block.
5) Using the dots as a guide, lay the ruler along the position of the incident ray and draw a line to represent this ray. Repeat with the reflected ray and the refracted ray.
6) Draw the normal to the flat surface of the block. Mark the angle of incidence i and the angle of refraction r. Measure these angles and record their values.
7) Replace the block and the ray box on a fresh sheet of paper.
8) Gradually move the ray round (increasing the angle of incidence) until the refracted ray travels along the surface of the block. (The angle of refraction is now 90°.)
9) Mark and draw the rays. The value of the angle of incidence is now the critical angle. Increase the angle of incidence still further and observe the reflected. Is there a reflected ray?
Applications of total internal reflection
Periscopes and binoculars: a periscope is constructed using two angled prisms. The light rays hit the inside surface of the prims at angles greater than to the critical angle. Therefore the light rays are internally reflected. Binoculars make use of the prism to reduce the length of the instrument and produce an erect image. These light rays are bent through 180° by each prism.
Optical fibres: An optic fibre is made of a core of high refractive index glass or plastic. Alight ray entering the fibre will be internally reflected at the surfaces. Optical fibres are used in telecommunications. They are cheaper and can carry more telephone signals. As no light can escape, it is difficult to intercept the signals as they travel.