Question

A ray of light is incident at $${50^o}$$ on the middle of one of the two mirros arranged at angle of $${60^o}$$ between them. The ray then touches the second mirror, get reflected back to the first mirror, making an angle of incidence of

A
50o
B
60o
C
70o
D
80o

Solution

The correct option is D $${70^o}$$Let required angle be $$\theta$$From geometry of figureIn $$\Delta ABC;\alpha=180^o-(60^o+40^o)=80^o$$$$\Rightarrow \beta =90^o-80^o=10^o$$In $$\Delta ABD,\angle A=60^o,\angle B=(\alpha+2\beta)$$$$=(80+2\times 10)=100^o$$ and $$\angle D=(90^o-\theta)$$$$\because \angle A+\angle B +\angle D=180^o \Rightarrow 60^o+100^o+(90^o-\theta)=180^o \Rightarrow \theta$$$$=70^o$$Physics

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