Question

Figure shows the graph of angle of deviation \( \delta \) versus angle of incidence \( i \) for a light ray striking a prism. The prism angle is 

• A. \( 30^\circ \)
• B. \( 45^\circ \)
• C. \( 60^\circ \)
• D. \( 75^\circ \)

Hint:

Prism graphs: Deviation curve symmetric. Use \( A = i_1 + i_2 - \delta \).

Answer 1

The Correct Option is B

Concept: For a prism: \[ \delta = i + e - A \] At minimum deviation: \[ i=e \Rightarrow \delta_{\min} = 2i - A \] Step 1: {\color{red}From graph.} Minimum deviation occurs at midpoint of symmetric curve. Given: \[ i_1=15^\circ,\quad i_2=60^\circ \] Symmetry point: \[ i = \frac{15+60}{2} = 37.5^\circ \] Step 2: {\color{red}Use deviation relation.} At endpoints deviation is same (shown 30° in graph). So: \[ \delta = i + e - A \] Using symmetry and equal deviation gives: \[ A = i_1 + i_2 - 2\delta \] Step 3: {\color{red}Substitute values.} \[ A = 15 + 60 - 30 = 45^\circ \]