Question:
To produce dispersion without deviation, a thin prism of angle \(15^\circ\) made of glass (refractive index 1.45) is combined with another prism made of glass of refractive index 1.75. The prisms are arranged such that refracting angles are in opposite direction. Find the angle of second prism.
To produce dispersion without deviation, a thin prism of angle \(15^\circ\) made of glass (refractive index 1.45) is combined with another prism made of glass of refractive index 1.75. The prisms are arranged such that refracting angles are in opposite direction. Find the angle of second prism.
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For no deviation condition, always equate \((\mu-1)A\) for both prisms.
Updated On: Jun 20, 2026
- \(10^\circ\)
- \(12^\circ\)
- \(6^\circ\)
- \(9^\circ\)
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The Correct Option is D
Solution and Explanation
Step 1: Condition for no deviation.
For no net deviation in combination of two prisms: \[ \delta_1 + \delta_2 = 0 \] For thin prisms: \[ \delta = (\mu - 1)A \]
Step 2: Apply condition.
\[ (\mu_1 - 1)A_1 = (\mu_2 - 1)A_2 \]
Step 3: Substitute values.
\[ (1.45 - 1)\times 15 = (1.75 - 1)\times A_2 \] \[ 0.45 \times 15 = 0.75 \times A_2 \]
Step 4: Solve.
\[ 6.75 = 0.75 A_2 \] \[ A_2 = 9^\circ \]
Step 5: Interpretation.
Second prism must exactly cancel deviation of first prism while still allowing dispersion due to different refractive indices.
Step 6: Final answer.
\[ \boxed{9^\circ} \]
For no net deviation in combination of two prisms: \[ \delta_1 + \delta_2 = 0 \] For thin prisms: \[ \delta = (\mu - 1)A \]
Step 2: Apply condition.
\[ (\mu_1 - 1)A_1 = (\mu_2 - 1)A_2 \]
Step 3: Substitute values.
\[ (1.45 - 1)\times 15 = (1.75 - 1)\times A_2 \] \[ 0.45 \times 15 = 0.75 \times A_2 \]
Step 4: Solve.
\[ 6.75 = 0.75 A_2 \] \[ A_2 = 9^\circ \]
Step 5: Interpretation.
Second prism must exactly cancel deviation of first prism while still allowing dispersion due to different refractive indices.
Step 6: Final answer.
\[ \boxed{9^\circ} \]
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