Question

The refracting angle of three prisms is $15^\circ$, but their refractive indices are 1.6, 1.5, and 1.4 respectively. If angles of deviation produced by them are $\delta_1, \delta_2,$ and $\delta_3$ respectively, then:

• A. $\delta_1>\delta_2>\delta_3$
• B. $\delta_1<\delta_2<\delta_3$
• C. $\delta_1 = \delta_2 = \delta_3$
• D. $\delta_1>\delta_2<\delta_3$

Hint:

For a prism of the same angle, deviation increases with the refractive index.

Answer 1

The Correct Option is A

Step 1: Formula for deviation at minimum deviation.
\[ \delta = (n - 1)A \] where $A$ = angle of prism, $n$ = refractive index.
Step 2: Calculate deviations.
For $n = 1.6$: \[ \delta_1 = (1.6 - 1)(15^\circ) = 0.6 \times 15 = 9^\circ. \] For $n = 1.5$: \[ \delta_2 = (1.5 - 1)(15^\circ) = 0.5 \times 15 = 7.5^\circ. \] For $n = 1.4$: \[ \delta_3 = (1.4 - 1)(15^\circ) = 0.4 \times 15 = 6^\circ. \]
Step 3: Conclusion.
\[ \delta_1>\delta_2>\delta_3. \] Hence, correct option is (A).