What is a total reflecting prism? State three actions that it can produce. Draw a diagram to show one action of the total reflecting prism.

Hint: A total reflecting prism is a right angled isosceles prism that has one angle equal to ${{90}^{0}}$ and other two angles equal to ${{45}^{0}}$. When light is incident normally on its faces, it suffers total internal reflection. It has many applications like it deviates light through ${{90}^{0}}$, erects an inverted image, etc.

Complete answer:
A total reflecting prism is a prism that reflects the light that falls normally on its faces, if angle of incidence is more than the critical angle (critical angle of glass is ${{42}^{0}}$), then total internal reflection takes place. It is a right angled isosceles prism that has one angle equal to ${{90}^{0}}$ and other two angles equal to ${{45}^{0}}$.
Three actions of total reflecting prism are,
1. It deviates light falling on any of its faces through ${{90}^{0}}$.
2. It deviates light falling on any of its faces through ${{180}^{0}}$.
3. It erects an image without any deviation.
The figure below shows one of the actions of the total reflecting prism, deviation of light through ${{180}^{0}}$.

The light from point P is incident normally on face AC of the prism and then falls on face AB at an angle of incidence ${{45}^{0}}$ and suffers total internal reflection as it is greater than critical angle of glass, i.e. ${{45}^{0}}\rangle {{42}^{0}}$, then again falls on face BC and suffers total internal reflection and similarly light from point Q suffers two total internal reflection and thus light is deviated through ${{180}^{0}}$.

Note:
The condition necessary for total internal reflection is that the angle of incident should be more than the critical angle of prism and value of critical angle of glass is ${{42}^{0}}$ should be kept in mind to solve prism and its applications related questions.