Two plane mirrors intersect at right angles. A laser beam strikes the first of t

Question

Two plane mirrors intersect at right angles. A laser beam strikes the first of them at a point d = 10.45cmfrom their point of intersection, as shown in the figure(Figure 1) .

Part A

For what angle of incidence at the first mirror will this ray strike the midpoint of the second mirror (which is s = 27.99cmlong) after reflecting from the first mirror?

Part B

What would need to be the length of the second mirror if the light were to just hit the edge of it after reflecting off the first mirror at an angle of reflection of29.3?.

Explanation / Answer

strikes mid point of B

angle A be adjacent to mirror 1 with reflected ray

tan A = (s/2) / d

tan A = (27.99/2) / 10.45

A = 53.25 degrees

so angle of reflection = 90 - 53.25 = 36.75 degrees

for plane mirror

angle of incidence = angle of reflection

so angle of incidence = 36.75 degrees

b) angle of reflection = 29.3 deg

angle adjacent to mirror = 90 - 29.3 = 60.7 degrees

tan(60.7) = s/d = s/10.45

s = 18.62 cm

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