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Laws of Reflection

Two place mir...

Question

Two place mirrors are inclined at an angle by $120^{o}$ , as the figure shows. If a ray strikes mirror $M_{1}$ , at a $65^{o}$ angle of incidence, at what angle $θ$ does it leave mirror $M_{2}$ .

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Solution

Since from laws of reflection $r_{1} = 65^{0}$ then $x = 90 - 65 = 25^{0}$
Hence from triangle
$x + y + 120^{0} = 180^{0}$
$x + y = 60^{0}$
$y = 35^{0}$
Hence $i_{2} = 90^{0} - 35^{0} = 55^{0}$
Hence from laws of reflection
$θ = i_{2} = 55^{0}$

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