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 = 11.53cm from their point of intersection, as shown in the figure (Figure 1) .

For what angle of incidence at the first mirror will this ray strike the midpoint of the second mirror (which is s = 25.86cm long) after reflecting from the first mirror?

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 of 37.1?.

Explanation / Answer

let theta_r is the angle of refraction at the first surface

so, tan(90-theta_r) = (s/2)/d

tan(90-theta_r) = (25.86/2)/11.53

90-theta_r = tan^-1(12.93/11.53)

90-theta_r = 48.27

theta_r = 90 - 48.27

= 41.73 degrees <<<<<<<----------Answer

in second case,

tan(90-37.1) = s/d

s = d*tan(52.9)

= 11.53*tan(52.9)

= 15.24 cm <<<<<<<----------Answer

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