Optical Geometry : "Fun with Laser Light"

Consider an rectangular glass board ABCDABCD , with surfaces ABAB, BCBC, CDCD are perfectly silvered. An small laser light is set in the corner AA (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 θ\theta with side ADAD and then totally reflected by surfaces DCDC , then CBCB , then BABA and finally refracted out from surface ADAD. If during this event , an quadrilateral and an triangle are traced out as shown & their point of intersection is PP, Such that Area of triangle( APTAPT ) is equal to that of quadrilateral( PQRSPQRS ).

Given that :


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

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

Note by Deepanshu Gupta
6 years, 1 month ago

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I get Tan(theta)= 4-√8 Can someone confirm

Suhas Sheikh - 3 years ago

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