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Question

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


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Solution

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:

δ=i-A+sin-1n·sinA-sin-1sinin

Here,

i=Angleofincidenceδ=AngleofdeflectionA=Angleofprismn=refractiveindex

  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 δ 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 δ decreases nonlinearly until it reaches its minimum value at i=e and then the value of δ 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.


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