Show by drawing ray diagrams how a totally reflecting glass prism can be used to deviate a ray of light through (i) `90^(@)` (ii) `180^(@)` and invert it.

Explanation

Totally Reflecting Prisms. We know the critical angle of glass is about `41^(@)`. If prism is so designed that its angles are `45^(@), 45^(@), 90^(@)`, it is said to be a totally reflecting prism. Its principal section is a right-angled isosceles triangle. Since the rays are incident at angle of `45^(@)` i.e., greater than critical angle of glass (`41^(@)` nearly), the rays suffer total internal reflection and the plane surfaces act as mirrors.

In figure (a), the reflecting face ac acts as a mirror which can produce a deviation of `90^(@)`. If we use the prism as shown in figure (b), both faces ab and be act as mirrors. The emergent rays get inverted and also a deviation of `180^(@)` is introduced between incident rays and emergent rays. If prism is placed as in Fig. (c), the face ac acts as a mirror and inverts the image without producing any deviation. Such prisms are called erecting prisms.