Question

Two plane mirrors arc inclined to each other such that a ray of light incident on the first mirror $(M_1)$ and parallel to the second mirror $(M_2)$ is finally reflected from the second mirror $(M_2)$ parallel to the first mirror $(M_1)$. The angle between the two mirrors will be :

• A. $90^{\circ}$
• B. $45^{\circ}$
• C. $75^{\circ}$
• D. $60^{\circ}$

Answer 1

The Correct Option is D

To solve this problem, we need to determine the angle between two plane mirrors M_1 and M_2 such that a ray reflecting from these mirrors meets the given conditions:

1. The ray of light is initially incident on mirror M_1.
2. The ray is parallel to mirror M_2 upon first incidence.
3. The ray is finally reflected from mirror M_2 and becomes parallel to mirror M_1.

To find the angle between these mirrors, we'll leverage the law of reflection, which states that the angle of incidence equals the angle of reflection. This problem is also commonly associated with theory regarding the adjacency angle between two mirrors:

Based on the given conditions, one should remember a well-known property of plane mirrors: if two mirrors are inclined at an angle \theta to each other, the number of images formed is given by:

n = \left(\dfrac{360^{\circ}}{\theta}\right) - 1

For finding the angle of inclination given that the ray finally reflects parallel, we utilize a different principle: if a ray of light strikes one mirror and is reflected in such a way that it becomes parallel to initial line of incidence, this effective condition tells us something about angles involved.

The required angle \theta between the two mirrors for the given reflective property is known from optics principles and can be directly stated as 60^{\circ} due to symmetrical and optical paths adjusting for such angle.

This means that for the ray to reflect in such way, the angle between mirrors should ensure both initial and eventual parallelism - a characteristic shown at 60^{\circ} angle for standard construction in conceptual optics.

Conclusion: The angle between the two mirrors that allows such a behavior for the light ray is 60^{\circ}.