Question

# Two identical plane mirrors of width w are placed a distance d apart with their mirrored surfaces parallel and facing each other. (a) A beam of light is incident at one end of one mirror so that the light just strikes the far end of the other mirror after reflection. Will the angle of incidence be $(1)\ \sin ^{-1}(w / d),(2)\ \cos ^{-1}(w / d),$ or $(3)\ \tan ^{-1}(w / d) ?$ (b) If d = 50 cm and w = 25 cm, what is the angle of incidence?

Solution

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a) Angle of incidence is the same as refliction angle for left mirror. If space between mirrors is d and their width is $\omega$, reflection angle then has relation:

\begin{aligned} \tan \theta_r&=\frac{\omega}{d} \end{aligned}

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