Question

A thin prism with angle 5° of refractive index 1.72 is combined with another prism of refractive index 1.9 to produce dispersion without deviation. The angle of second prism is :

• A. 4.5°
• B. 5°
• C. 4°
• D. 6°

Hint:

"Dispersion without deviation" requires the deviations to cancel out. "Deviation without dispersion" requires the angular dispersions (\(\delta_v - \delta_r\)) to cancel out.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
For "dispersion without deviation," the net deviation produced by the combination of the two prisms must be zero.
Step 2: Key Formula or Approach:
1. Deviation for a thin prism: \(\delta = (\mu - 1)A\).
2. Condition: \(\delta_1 + \delta_2 = 0 \implies (\mu_1 - 1)A_1 = (\mu_2 - 1)A_2\).
Step 3: Detailed Explanation:
Given: \(A_1 = 5^\circ\), \(\mu_1 = 1.72\), \(\mu_2 = 1.9\). \[ (1.72 - 1) \times 5^\circ = (1.9 - 1) \times A_2 \] \[ 0.72 \times 5 = 0.9 \times A_2 \] \[ 3.6 = 0.9 \times A_2 \] \[ A_2 = \frac{3.6}{0.9} = 4^\circ \]
Step 4: Final Answer:
The angle of the second prism is 4°.