MHT CET · Physics · Ray Optics

Three immiscible transparent liquids with uniform refractive indices \(\frac{3}{2}, \frac{4}{3}\) and \(\frac{6}{5}\) are arranged one on top of another. The depths of the liquids are 3 cm 4 cm and 6 cm respectively. The apparent depth of the vessel is

A 10 cm
B 9 cm
C 8 cm
D 7 cm

Verified Solution

Answer & Solution

Correct Answer

(A) 10 cm

Step-by-step Solution

Detailed explanation

\(\mu=\frac{\text { Real depth }(R)}{\text { Apparent depth }} \Rightarrow \text { Apparent depth }=\frac{R}{\mu}\)
For vessel,
\(\begin{aligned}
\text { Apparent depth } & =\frac{R_1}{\mu_1}+\frac{R_2}{\mu_2}+\frac{R_3}{\mu_3} \\
& =\frac{3}{3 / 2}+\frac{4}{4 / 3}+\frac{6}{6 / 5} \\
& =2+3+5 \\
\text { Apparent depth } & =10 \mathrm{~cm}
\end{aligned}\)

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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