AP EAMCET · PHYSICS · Ray Optics

A needle is lying at the bottom of a water tank of height \(12 \mathrm{~cm}\). The apparent depth of the needle measured by a microscope is \(9 \mathrm{~cm}\). If the water is replaced by a liquid of refractive index of 1.5 of same height, the distance through which the microscope has to be moved to focus the needle again is

A \(1.2 \mathrm{~cm}\)
B \(1.1 \mathrm{~cm}\)
C \(1 \mathrm{~cm}\)
D \(1.33 \mathrm{~cm}\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(1 \mathrm{~cm}\)

Step-by-step Solution

Detailed explanation

For water, real depth \(=12 \mathrm{~cm}\) Apparent depth \(=9 \mathrm{~cm}\) Since, refractive index, \(\mu_w=\frac{\text { Real depth }}{\text { Apparent depth }}\) \(\Rightarrow \quad \mu_w=\frac{12}{9}\) when water is replaced by liquid of refractive index \(\mu=1.5\), we…

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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