Question:
A needle is lying at the bottom of a water tank of height \(12\,\text{cm}\). The apparent depth of the needle measured by a microscope is \(9\,\text{cm}\). If the water is replaced by a liquid of refractive index \(1.5\) of same height, the distance through which the microscope has to be moved to focus the needle again is
A needle is lying at the bottom of a water tank of height \(12\,\text{cm}\). The apparent depth of the needle measured by a microscope is \(9\,\text{cm}\). If the water is replaced by a liquid of refractive index \(1.5\) of same height, the distance through which the microscope has to be moved to focus the needle again is
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For viewing an object through a liquid,
\[
\text{apparent depth}=\frac{\text{real depth}}{\mu}
\]
where \(\mu\) is the refractive index of the liquid.
Updated On: Jun 22, 2026
- \(1.2\,\text{cm}\)
- \(1.1\,\text{cm}\)
- \(1\,\text{cm}\)
- \(1.33\,\text{cm}\)
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The Correct Option is C
Solution and Explanation
Step 1: Use the formula for apparent depth.
For a liquid, \[ \mu=\frac{\text{real depth}}{\text{apparent depth}} \] Given real depth of water tank is \[ 12\,\text{cm} \] Apparent depth in water is \[ 9\,\text{cm} \]
Step 2: Find apparent depth in the new liquid.
For the new liquid, \[ \mu=1.5 \] So, \[ \text{apparent depth}=\frac{\text{real depth}}{\mu} \] \[ =\frac{12}{1.5} \] \[ =8\,\text{cm} \]
Step 3: Find the shift in microscope position.
Initially, the microscope focuses the needle at apparent depth \[ 9\,\text{cm} \] After replacing water by liquid, the apparent depth becomes \[ 8\,\text{cm} \] Therefore, the microscope has to be moved through \[ 9-8=1\,\text{cm} \]
Step 4: Final conclusion.
Hence, the distance through which the microscope has to be moved is \[ \boxed{1\,\text{cm}} \]
For a liquid, \[ \mu=\frac{\text{real depth}}{\text{apparent depth}} \] Given real depth of water tank is \[ 12\,\text{cm} \] Apparent depth in water is \[ 9\,\text{cm} \]
Step 2: Find apparent depth in the new liquid.
For the new liquid, \[ \mu=1.5 \] So, \[ \text{apparent depth}=\frac{\text{real depth}}{\mu} \] \[ =\frac{12}{1.5} \] \[ =8\,\text{cm} \]
Step 3: Find the shift in microscope position.
Initially, the microscope focuses the needle at apparent depth \[ 9\,\text{cm} \] After replacing water by liquid, the apparent depth becomes \[ 8\,\text{cm} \] Therefore, the microscope has to be moved through \[ 9-8=1\,\text{cm} \]
Step 4: Final conclusion.
Hence, the distance through which the microscope has to be moved is \[ \boxed{1\,\text{cm}} \]
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