# Deviation and Dispersion of Light by a Prism

## Problems from IIT JEE

**Problem (IIT JEE 2008): **
Two beams of red and violet colours are made to pass separately through a prism (angle of the prism is 60 degree). In the position of minimum deviation, the angle of refraction will be,

- 30 degree for both the colours.
- greater for the violet colour.
- greater for the red colour.
- equal but not 30 degree for both the colours.

**Solution: **
At the angle of minimum deviation ($\delta_m$), angle of incidence is equal to the angle of emergence, the angle of refraction ($r$) is equal to half of the prism angle ($A$) and ray inside the prism is parallel to the prism base. Further, refractive index is given by,
\begin{align}
\label{aga:eqn:1}
\mu=\frac{\sin\frac{A+\delta_m}{2}}{\sin\frac{A}{2}},
\end{align}
and the angle of incidence by,
\begin{align}
\label{aga:eqn:2}
i=\frac{A+\delta_m}{2}.
\end{align}
From above equations, $\delta_m$ and $i$ depend on $\mu$ (colours). However, for the given prism, $r=A/2={30}\;\mathrm{degree}$ is independent of $\mu$. Readers are encouraged to find $\delta_m$ and $i$ for red and violet colours if $\mu_\text{red}=1.514$ and $\mu_\text{violet}=1.523$.