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
3 years ago

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