To measure the critical angle and refractive index of the material of a prism

To measure the critical angle and refractive index of the material of a prism

An equilateral glass prism ABC is placed on a sheet of paper and its outline drawn on the paper with the aid of a ruler in a manner similar to that described for the glass block on page 249. An object pin 0 is then stuck in the paper touching the side CA and its image is viewed through the side Be (Fig. 23.14). Light enters the eye after internal reflection from AB, followed by refraction through Be.

If the eye is well to the left the image seen is weak owing to the fact that the light has undergone only partial internal reflection. If, however, the eye is well to the right the image is bright, since total internal reflection has occurred. Therefore, as the eye moves from left to right through the critical position the image suddenly becomes brighter. The emergent ray for this position is located by pins PI and P2. The prism is then removed and PIP 2 joined to cut BC in D. Because AB acts as a reflecting surface the ray ED appears to be coming from I,
which is the image of 0 in AB. Rays OE and ED can therefore be located as follows. Draw OMI perpendicular to AB, making 1M = OM. Join ID to cut AB in E. Join OE. Then angle OED = twice the critical angle c. Hence c can be found and the
refractive index calculated.