# 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
5 years, 10 months ago

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

- 2 years, 9 months ago