Two plane mirrors and are arranged at an angle as shown in the figure. An incident ray parallel to strikes . Find the angle such that the light ray retraces its path after 2 reflections.
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Question

Two plane mirrors  and  are arranged at an angle  as shown in the figure. An incident ray parallel to  strikes . Find the angle  such that the light ray retraces its path after 2 reflections.?

Answer

Problem

Two plane mirrors, A and B, are arranged at an angle θ as shown in the figure below. An incident ray parallel to AB strikes A. Find the angle θ such that the light ray retraces its path after 2 reflections.

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Solution

Explanation of Reflection

When a light ray is incident on a plane mirror, it is reflected back in such a way that the angle of incidence is equal to the angle of reflection. This is known as the law of reflection. The incident ray, the reflected ray, and the normal to the mirror all lie in the same plane.

Reflection of Incident Ray

As the incident ray is parallel to the mirror AB, it will be reflected at an angle equal to the angle of incidence which is also equal to the angle θ. The reflected ray will be parallel to the mirror AB.

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Reflection of Reflected Ray

The reflected ray from mirror A will strike mirror B and will be reflected again. As the angle of incidence is equal to the angle of reflection, the angle of incidence at mirror B will also be θ. Therefore, the angle between the reflected ray from mirror A and mirror B will be 2θ.

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Retracing the Path

For the light ray to retrace its path, the angle between the reflected ray from mirror A and mirror B should be equal to the angle between the incident ray and mirror A. As the incident ray is parallel to mirror AB, the angle between the incident ray and mirror A is 90°. Therefore, we can write:

2θ = 90°

θ = 45°

Conclusion

The angle between the mirrors should be 45° for the light ray to retrace its path after 2 reflections.

Answer

I don't know the answer sorry

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