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Question

Two plane mirrors are inclined to each other at an angle of 700. A ray is incident on one mirror at an angle θ. The ray reflected from this mirror falls on the second mirror from where it is reflected parallel to the first mirror. Determine the value of θ.

A
θ=700
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B
θ=450
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C
θ=500
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D
θ=400
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Solution

The correct option is C θ=500

I=θ

r=θ for first mirror

Angle between the reflected ray and the first mirror will be 90θ

Angle between the two mirrors = 70o

Since the emergent ray comes out parallel to the first mirror, it also makes 70o with the second mirror. Thus e= angle of reflection for second mirror= 9070=20o

The reflected ray from first mirror, striking the second mirror makes a triangle with the two mirrors. Angle of incidence of 2nd mirror= angle of incidence for 2nd mirror= 20o

Thus the angle between the reflected ray from first mirror and the second mirror= 90-20= 70o

Since, it makes a triangle, 180=70+70+(90θ)

θ=50o


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