Question

In total reflecting prism, the angle between its two refracting surfaces is:
A. ${{90}^{0}}$
B. ${{45}^{0}}$
C. ${{30}^{0}}$
D. ${{60}^{0}}$

Answer 1

Hint: A total reflecting prism is a prism in which, when light falls normally on any of the surfaces, it is internally reflected totally. This happens because the prism is constructed in such a way that the angle of incidence becomes more than the critical angle required for total internal reflection.

Complete step by step answer:
A total reflecting prism is a special kind of prism which can internally reflect light that falls normally on any one of its surfaces. This becomes possible since the prism is constructed in such a way so that the angle of incidence is more than the critical angle that is required for total internal reflection.
By placing the total reflecting prism in different orientations, a total reflecting prism can be used to deviate a ray of light through ${{180}^{0}}$ or ${{90}^{0}}$. It can also be used to produce an inverted image of an object without deviation of its path.
A total reflecting prism requires that its angles be a particular value. The angle between the two refracting edges is ${{90}^{0}}$ while the other two angles in the triangular face are equal to ${{45}^{0}}$ each. Hence, in essence, a total reflecting prism has a triangular face that is an isosceles triangle.
Hence the correct option is A) ${{90}^{0}}$.

Note: Students should properly know of the various purposes of a total reflecting prism and the orientations in which the prism be placed to get the desired nature of the image, or to deviate light by a certain angle.
Students who do not know the correct answer can often guess that the angle should be ${{60}^{0}}$, with the triangular face being an equilateral triangle, since it is the most unique form of a triangle. However, students must refrain from such wild guesses, especially in competitive exams, where there is a possibility of negative marking.