Question

At the lowest point of the plot of angle of deviation versus the angle of incidence of a triangular prism, the angle of incidence is equal to

• A. the angle of refraction at the first face
• B. the angle of refraction at the second face
• C. the angle of emergence
• D. the angle of prism
• E. half of the angle of prism

Hint:

At minimum deviation in a prism: \[ i = e \quad \text{and} \quad r_1 = r_2 \] This symmetry simplifies many prism problems.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
The question refers to the condition of minimum deviation for a light ray passing through a prism. The angle of deviation (\(\delta\)) is the angle between the incident ray and the emergent ray. When we plot the angle of deviation against the angle of incidence (\(i\)), we get a characteristic curve. The lowest point of this curve corresponds to the angle of minimum deviation (\(\delta_{min}\)).
Step 2: Key Formula or Approach:
The condition for minimum deviation is achieved when the light ray passes symmetrically through the prism. This symmetry implies two key conditions:
1. The angle of incidence (\(i\)) is equal to the angle of emergence (\(e\)).
\[ i = e \] 2. The angle of refraction at the first face (\(r_1\)) is equal to the angle of incidence at the second face (\(r_2\)).
\[ r_1 = r_2 = r \] Also, the angle of the prism A is given by \( A = r_1 + r_2 \), which simplifies to \( A = 2r \) at minimum deviation.
Step 3: Detailed Explanation:
The question asks what the angle of incidence (\(i\)) is equal to at the lowest point of the \( \delta \) vs \( i \) plot. This lowest point is the position of minimum deviation.
As established from the principle of symmetry for minimum deviation, the angle of incidence must be equal to the angle of emergence.
\[ i = e \] Therefore, at the point of minimum deviation, the angle of incidence is equal to the angle of emergence.
Step 4: Final Answer:
At the condition of minimum deviation, the angle of incidence is equal to the angle of emergence. This corresponds to option (C).