Question:
A thin prism \( P_1 \) of angle 4° and refractive index 1.54° is combined with another thin prism \( P_2 \) of refractive index 1.72 to produce dispersion without deviation. The angle of \( P_2 \) is
A thin prism \( P_1 \) of angle 4° and refractive index 1.54° is combined with another thin prism \( P_2 \) of refractive index 1.72 to produce dispersion without deviation. The angle of \( P_2 \) is
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For two prisms combined to produce dispersion without deviation, their deviations must cancel each other. Use the formula \( \delta = (\mu - 1) A \) for each prism to solve for the angle of the second prism.
Updated On: Apr 22, 2026
- 4°
- 5.33°
- 2.6°
- 3°
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The Correct Option is D
Solution and Explanation
Step 1: Understanding the dispersion condition.
When two prisms are combined to produce dispersion without deviation, the total deviation produced by both prisms must cancel each other out. This means that the deviation produced by the first prism (\( \delta_1 \)) is exactly balanced by the deviation produced by the second prism (\( \delta_2 \)). The deviation for a prism is given by: \[ \delta = (\mu - 1) A \] where \( \mu \) is the refractive index of the prism, and \( A \) is the angle of the prism.
Step 2: Setting up the equation.
For no deviation, the deviations must cancel out: \[ (\mu_1 - 1) A_1 = (\mu_2 - 1) A_2 \] Substituting the given values: \[ (1.54 - 1) 4 = (1.72 - 1) A_2 \] \[ 0.54 \times 4 = 0.72 \times A_2 \] \[ A_2 = \frac{2.16}{0.72} = 3 \, \text{°} \]
Step 3: Conclusion.
Thus, the angle of \( P_2 \) is 3°. Therefore, the correct answer is (4).
When two prisms are combined to produce dispersion without deviation, the total deviation produced by both prisms must cancel each other out. This means that the deviation produced by the first prism (\( \delta_1 \)) is exactly balanced by the deviation produced by the second prism (\( \delta_2 \)). The deviation for a prism is given by: \[ \delta = (\mu - 1) A \] where \( \mu \) is the refractive index of the prism, and \( A \) is the angle of the prism.
Step 2: Setting up the equation.
For no deviation, the deviations must cancel out: \[ (\mu_1 - 1) A_1 = (\mu_2 - 1) A_2 \] Substituting the given values: \[ (1.54 - 1) 4 = (1.72 - 1) A_2 \] \[ 0.54 \times 4 = 0.72 \times A_2 \] \[ A_2 = \frac{2.16}{0.72} = 3 \, \text{°} \]
Step 3: Conclusion.
Thus, the angle of \( P_2 \) is 3°. Therefore, the correct answer is (4).
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