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# Optical Geometry : "Fun with Laser Light"

Consider an rectangular glass board $$ABCD$$ , with surfaces $$AB$$, $$BC$$, $$CD$$ are perfectly silvered. An small laser light is set in the corner $$A$$ (negligible dimensions) . Now just for fun , this laser light is set in such a way so that light ray first travel from A making an angle $$\theta$$ with side $$AD$$ and then totally reflected by surfaces $$DC$$ , then $$CB$$ , then $$BA$$ and finally refracted out from surface $$AD$$. If during this event , an quadrilateral and an triangle are traced out as shown & their point of intersection is $$P$$, Such that Area of triangle( $$APT$$ ) is equal to that of quadrilateral( $$PQRS$$ ).

Given that :

$$AB=CD=2(BC)=2(AD)$$

$$\text{Laws of reflection holds perfectly}$$.

Then find that particular angle $$\theta$$ in degrees or just simply prove that $$\tan { \theta } =\cfrac { a-\sqrt { b } }{ c }$$ and find $$a+b+c$$ , for which such event is possible.

Note by Deepanshu Gupta
1 year, 7 months ago