The expected graphical representation of the variation of angle of deviation 'δ' with angle of incidence 'i' in a prism is :

Solution

Physics sir · 4 steps

As i increases, δ first falls, reaches a minimum, then rises again, so look for the U-shaped curve.

1. Deviation relation. For a prism of angle A, the deviation depends on both the angle of incidence i and the angle of emergence e.

   δ = i + e - A

2. How δ changes. At small i the ray emerges at a large e, so δ is large. As i increases, e decreases quickly and δ falls. It reaches its minimum δₘ when i = e, which is when the ray passes symmetrically through the prism. Beyond that point δ rises again.
3. Shape of curve. So the graph is a U-shaped curve with a single minimum and no part of it touches zero. It is not symmetric: the curve rises more slowly to the right of the minimum than it falls on the left.
4. So. Graph (b), which falls to a minimum and then rises, is the correct δ versus i graph.

The idea to keep. For a prism, δ against i always gives a U-shaped curve with one minimum. At that minimum the ray passes symmetrically, with i = e. This is the δ_m that appears in the formula for μ.

Answer from the NTA final answer key. Solution by PrepWiser.