Question

A rectangular tank of depth 4 m is full of water of refractive index \(\frac 43\). When viewed from the top, the bottom of the tank is seen at a depth of

• A. 3 m
• B. 2 m
• C. 1.33 m
• D. 1 m

Answer 1

The Correct Option is A

The refractive index of a medium is the ratio of the real depth to the apparent depth. 

In this case, we are given that the real depth of the tank is 4 m and the refractive index of water is $\frac{4}{3}$. 

We want to find the apparent depth, which we will call $d_a$. 

The refractive index is given by $$ n = \frac{\text{real depth}}{\text{apparent depth}} = \frac{d_r}{d_a} $$ 

In this case, we have $n = \frac{4}{3}$ and $d_r = 4$. So $$ \frac{4}{3} = \frac{4}{d_a} $$ Cross-multiplying, we get $$ 4d_a = 12 $$ $$ d_a = \frac{12}{4} = 3 $$ 

So, the apparent depth is 3 m.