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: Understand minimum deviation condition.
The lowest point in deviation curve corresponds to minimum deviation condition.

Step 2: Recall the symmetry condition.
At minimum deviation: \[ i = e \] where \( i \) is angle of incidence and \( e \) is angle of emergence.

Step 3: Explain physical reason.
Light travels symmetrically through the prism at minimum deviation.

Step 4: Relation of internal angles.
Angles of refraction inside prism become equal: \[ r_1 = r_2 \]

Step 5: Use standard prism relation.
\[ A = r_1 + r_2 \Rightarrow r_1 = r_2 = \frac{A}{2} \]

Step 6: Key conclusion.
Symmetry implies: \[ i = e \]

Step 7: Final conclusion.
Thus, \[ \boxed{i = e} \] Therefore, the correct option is \[ \boxed{(3)\ \text{angle of emergence}} \]