# (a) Plot a graph for angle of deviation as a function of angle of incidence for a triangular prism.(b) Derive the relation for the refractive index of the prism in terms of the angle of minimum deviation and angle of prism.

(a) A graph for the angle of deviation as a function of angle of incidence for a triangular prism;

(b) We know that,

$n_{21}=\frac{\sin i}{\sin r}$

From the figure,

$\\

At minimum deviation i.e, $\delta =\delta m,$ $i=e$ and $r_{1}=r_{2}=r$

$\therefore r=\frac{A}{2}$ _______(i)

From the figure, we have

$\delta =(i-r_{1})+(e-r_{2})$

$\therefore \delta m =(i+e)+(r_{1}+r_{2})$

$i=\frac{A+\delta m}{2}$_______(ii)

From eqn. (1) and (2) , we have,

$n_{21}=\frac{\sin i}{\sin r}=\frac{sin\frac{A+\delta m}{2}}{\sin \frac{A}{2}}$

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