MHT CET · Physics · Ray Optics

A glass prism deviates the red and violet rays through \(9^{\circ}\) and \(11^{\circ}\) respectively. A second prism of equal angle deviates them through \(11^{\circ}\) and \(13^{\circ}\) respectively. The ratio of dispersive power of second nrism to first prism is

A \(5: 6\)
B \(6: 5\)
C \(9: 13\)
D \(13: 9\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(5: 6\)

Step-by-step Solution

Detailed explanation

\(\therefore \quad\) Dispersive Power of Prism:
\(
\begin{aligned}
& \omega=\frac{\delta_v-\delta_r}{\delta_y} \\
& \delta_y=\frac{\delta_v+\delta_r}{2}=\frac{11+9}{2}
\end{aligned}
\)
\(\therefore \quad\) For first Prism,
\(
\begin{aligned}
\omega_1 & =\frac{2(11-9)}{11+9} \\
& =\frac{1}{5}
\end{aligned}
\)
For Second Prism:
\(
\begin{aligned}
\omega_2 & =\frac{2(13-11)}{13+11} \\
& =\frac{1}{6}
\end{aligned}
\)
Ratio:
\(
\frac{\omega_2}{\omega_1}=\frac{\frac{1}{6}}{\frac{1}{5}}=\frac{5}{6}
\)
\(\therefore \quad\) The ratio is \(5: 6\).

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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