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 (same height), the distance through which the microscope has to be moved to focus the needle again is:

• A. 1.2 cm
• B. 1.1 cm
• C. 1 cm
• D. 1.33 cm

Hint:

Apparent depth = \( \frac{\text{Real depth}}{\text{Refractive index}} \). Difference gives the required shift.

Answer 1

The Correct Option is C

Apparent depth: \[ \text{Apparent depth} = \frac{\text{Real depth}}{\mu} \] From original water layer: \[ 9 = \frac{12}{\mu_w} \Rightarrow \mu_w = \frac{12}{9} = \frac{4}{3} \] With new liquid of refractive index 1.5: \[ \text{New apparent depth} = \frac{12}{1.5} = 8\, \text{cm} \] Shift in microscope = old apparent depth − new apparent depth: \[ 9 - 8 = 1\, \text{cm} \]