Question

A prism made up of flint glass is such that the incident ray does not emerge from the second surface. Critical angle for flint glass is $36^{\circ} .$ Then, refracting angle $A$ must be
(A) \[{{37}^{{}^\circ }}\]
(B) \[{{54}^{{}^\circ }}\]
(C) \[{{71}^{{}^\circ }}\]
(D) \[{{73}^{{}^\circ }}\]

Answer 1

Hint: The angle of deviation is defined as the angle derived from the difference between the angle of incidence and the angle of refraction generated by a light ray that travels from one medium to another with a different refractive index.

Complete Step-by-Step Solution:
The angle of the prism is the angle between the two surfaces of the prism from which the light enters the prism and exits after refraction from the light. The angle of the prism is the angle between the prism's two adjacent rectangular surfaces. The angle of a prism is \[{{60}^{{}^\circ }}\] for an equilateral prism.
The refracting angle in the prism must be more than twice the critical angle of the prism material in order for total internal reflection to occur. In this case, the critical angle for flint glass is \[{{36}^{{}^\circ }}\], so the angle of refraction A must be greater than twice the critical angle, which must be greater than \[{{72}^{{}^\circ }}\].
The refracting angle $A$ must be \[{{73}^{{}^\circ }}\].

Hence the correct option is (D).

Additional Information:
The angle of the prism or the prism angle is the angle between its two lateral faces. It makes the emerging ray bend at an angle to the direction of the incident ray when the light ray is allowed to pass through the prism. This is known as the angle of deviation of the prism.

Note:
Total internal reflection is the complete reflection of a ray of light in a medium such as water or glass back into the medium from the surrounding surfaces. If the angle of incidence is greater than a certain limiting angle, called the critical angle, the phenomenon happens.