Question

A bucket of total height 60 cm is half filled with a liquid of refractive index 1.5 and half with another liquid of refractive Index 2. The apparent depth of the bucket for an observer directly above the bucket is

• A. 45 cm
• B. 30 cm
• C. 35 cm
• D. 40 cm

Answer 1

The correct option is C 35 cm

Given: A bucket of total height 60 cm is half filled with a liquid of refractive index 1.5 and half with another liquid of refractive Index 2.

To find the apparent depth of the bucket for an observer directly above the bucket

Solution:

As per the given criteria,

Depth of the bucket, $d=60cm$

Refractive index of the liquids, $m{u}_1=1.5,{\mu }_2=2$

We know,

Refractive index, $\mu =\frac{\text{Real depth}}{\text{Apparent Depth}}$

Bucket is half filled with liquid of refractive index, ${\mu }_1=1.5$

Therefore, Apparent Depth, $d_1=\frac{\frac{60}{2}}{1.5}=20cm$

Other half is filled with liquid of refractive index, ${\mu }_1=2$

Therefore, Apparent Depth, $d_2=\frac{\frac{60}{2}}{2}=15cm$

Total apparent depth,

$D=d_1+d_2⟹D=20+15=35cm$

is the required apparent depth of the bucket for an observer directly above the bucket