Question

A ray of light falls on the surface of a spherical glass paper weight making an angle $\alpha$ with the normal and is refracted in the medium at an angle $\beta$. The angle of deviation of the emergent ray from the direction of the incident ray is

• A. $(\alpha -\beta )$
• B. $2(\alpha -\beta )$
• C. $\frac{(\alpha -\beta )}{2}$
• D. $(\alpha +\beta )$

Answer 1

The correct option is B $2(\alpha -\beta )$

From figure it is clear that $\Delta OBC$ is an isosceles triangle ,
Hence $\angle OCB=\beta$ and emergent angle is $\alpha$
Also sum of two in terior angles = exterior angle
$\therefore \delta =(\alpha -\beta )+(\alpha -\beta )=2(\alpha -\beta )$