Question

A graph is plotted between the angle of deviation $\delta$ and angle of incidence $i$ for a prism. The nearly correct graph is

Answer 1

The graph between the angle of deviation and angle of incidence:

Explanation:

From the relation of the angle of incidence to the angle of deflection:

$\delta =i-A+{\sin }^{-1}\left(n·\sin \left(A-{\sin }^{-1}\left(\frac{\sin i}{n}\right)\right)\right)$

Here,

$$\begin{gathered} i=Angleofincidence \\ \delta =Angleofdeflection \\ A=Angleofprism \\ n=refractiveindex \end{gathered}$$

1. When we plot the graph of the above relation it comes out to be of parabolic nature with a minimum.
2. The minimum value of angle of deviation $\delta$ is at the point where $i=e$ i.e. angle of incidence is equal to the angle of emergence.
3. In the given graph as the value of the angle of incidence $i$ increases the value of the angle of deviation $\delta$ decreases nonlinearly until it reaches its minimum value at $i=e$ and then the value of $\delta$ starts increasing and hence form a downward parabola.

Hence, the graph between angle of incidence and angle of deviation is a parabola with minimum deviation at $i=e$.