Question

For a thin symmetric prism made of glass (refractive index \(1.5\)), the ratio of incident angle and minimum deviation will be _____.

• A. \(3:4\)
• B. \(3:2\)
• C. \(2:1\)
• D. \(1:2\)

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
For a thin prism with prism angle \(A\), the angle of minimum deviation is \(\delta_m = (\mu - 1)A\).
At minimum deviation, the angle of incidence \(i\) is given by \(i = \frac{A + \delta_m}{2}\).
Step 2: Key Formula or Approach:
1. \(\delta_m = (1.5 - 1)A = 0.5 A = \frac{A}{2}\).
2. \(i = \frac{A + A/2}{2} = \frac{3A}{4}\).
Step 3: Detailed Explanation:
Given refractive index \(\mu = 1.5\).
Deviation \(\delta_m = (\mu - 1)A = (1.5 - 1)A = 0.5 A\).
The incident angle at minimum deviation is \(i = \frac{A + \delta_m}{2} = \frac{A + 0.5A}{2} = 0.75 A\).
Now, find the ratio \(i : \delta_m\):
\[ \frac{i}{\delta_m} = \frac{0.75 A}{0.5 A} = \frac{3/4}{1/2} = \frac{3}{2} \].
Step 4: Final Answer:
The ratio of incident angle to minimum deviation is 3 : 2.