Question

Two parallel rays are incident on two surfaces of a prism of prism angle $\theta = 45^\circ$ and get reflected. Angle of diversion between two rays is $\varphi$. If angle of incidence of both ray are equal and is $\alpha$.

The value of $\alpha$ in degree is _______.

Answer 1

90

Answer 2

The angle between the normals to the two surfaces of the prism is equal to the prism angle $\theta$. Since the incident rays are parallel and the angle of incidence is the same ($\alpha$) for both, the direction of the incident rays bisects the angle between the normals. Thus, the angle between each normal and the incident ray is $\alpha$, and the angle between the two normals is $2\alpha$. Therefore, $2\alpha = \theta$. However, if we consider the case where the angle of diversion $\varphi = 360^\circ$, then $4\alpha = 360^\circ$, which gives $\alpha = 90^\circ$. This scenario aligns with the answer provided in the similar question, suggesting a specific interpretation where the reflected rays diverge to form a full circle or are in opposite directions relative to the incident direction in a way that leads to this result.