Question

A microscope is focused on an object at the bottom of a bucket If liquid with refractive index $\frac{5}{3}$ is poured inside the bucket, then microscope have to be raised by $30\, cm$ to focus the object again The height of the liquid in the bucket is :

• A. 12cm
• B. 18cm
• C. 50cm
• D. 75cm

Hint:

The apparent depth decreases when the refractive index increases, and the object appears to be closer to the surface.

Answer 1

The Correct Option is D

The apparent depth \( d' \) when viewed through a liquid is related to the real depth \( d \) by the refractive index \( n \) of the liquid: \[ d' = \frac{d}{n} \] In this case, the microscope had to be raised by 30 cm, which means the apparent depth has been reduced by 30 cm. Thus, the relation becomes: \[ d - d' = 30 \, \text{cm} \] Substitute \( d' = \frac{d}{n} \) and \( n = \frac{5}{3} \): \[ d - \frac{d}{\frac{5}{3}} = 30 \] \[ d - \frac{3d}{5} = 30 \] \[ \frac{2d}{5} = 30 \] \[ d = 75 \, \text{cm} \]