Question

A ray of light strikes a plane mirror at an angle of incidence ${45}^0$ as shown in figure. After reflection, the ray passes through a prism of refractive index 1.5 whose apex angle is $4^0$. Through what angle in degree must be mirror be rotated if the total deviation of the ray be ${90}^0$ ?

Answer 1

The deviation produced by small angled prims, ${\delta }_1=\left({\mu }_{1}1\right)\alpha =\left(1.51\right)4^o=2^o$ (always).

Deviation caused by mirror, ${\delta }_2=180o2i={180}^{o}2\times {45}^o={90}^o$.

Net deviation produced by system = ${\delta }_1+{\delta }_2=2^o+{90}^o={92}^o$

This is more than 90${}^o$. Greater is angle of incidence on mirror, smaller is the deviation. If $\beta$ is the angle of rotation of mirror in clockwise direction to increase angle of incidence, then deviation produced by mirror will be ${180}^{o}2({45}^o+\beta )={90}^{o}2\beta$

$\therefore$ Total deviation produced $={90}^{o}2\beta +2^o={92}^{o}2\beta \therefore$ Given ${92}^{o}2\beta ={90}^o\Rightarrow \beta =1^o$