Question

Two mirrors are touching so they have an angle of 19.4 degrees with one another. A light ray is incident on the first at an angle of 45.8 degrees with respect to the normal to the surface. What is the angle of reflection from the second surface?

Answer 1

In plane mirrors we know that

Angle of incidence = Angle of reflection. So

i = r

i = angle of incidence of light ray on M1 = 45.8 deg

r = angle of reflection of light ray on M1 = 45.8 deg

Now from trigonometry:

90 - r = 90 - 45.8 = 44.2 deg

Given that = angle between both mirrors = 19.4 deg, So

In a triangle

+ + 90 - r = 180 deg

= 180 - 90 + r -

= 90 + 45.8 - 19.4 = 116.4 deg

i1 = incidence angle of ray on M2 = 116.4 - 90 = 26.4 deg

Since i1 = r1, So

r1 = reflection angle of ray on M2 (second surface) = 26.4 deg

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