MHT CET · Physics · Ray Optics

A plane mirror is placed at the bottom of a tank containing a liquid of refractive index ' \(\mu\) ', ' p ' is a small object at a height ' \(h\) ' above the mirror. An observer ' \(O\) ' vertically above ' \(p\) ' outside the liquid sees ' \(p\) ' and the image in a mirror. The apparent distance between these two will be

A \(2 \mu \mathrm{~h}\)
B \(\frac{2 h}{\mu}\)
C \(\frac{2 \mathrm{~h}}{(\mu-1)}\)
D \(\mathrm{h}\left(1+\frac{1}{\mu}\right)\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{2 h}{\mu}\)

Step-by-step Solution

Detailed explanation

Let the apparent depth of P be \(\mathrm{x}_1\) and the apparent depth of the image of P be \(\mathrm{x}_2\).
\(\therefore \quad \mathrm{x}_1=\frac{\mathrm{d}-\mathrm{h}}{\mu}\) and \(\mathrm{x}_2=\frac{\mathrm{d}+\mathrm{h}}{\mu}\)
\(\therefore \quad\) Apparent distance between P and its image is
\(\begin{aligned}
\dot{x}_2-x_1 & =\frac{d+h}{\mu}-\frac{(d-h)}{\mu} \\
& =\frac{d+h-d+h}{\mu}=\frac{2 h}{\mu}
\end{aligned}\)

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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