Question

A rectangular tank of depth 2 m is full of water of refractive index \(\frac{4}{3 }\) When viewed from the top, the bottom of the tank is seen at a depth of 

• A. 2.66 m
• B. 1.5 m
• C. 1.33 m
• D. 3.33 m

Answer 1

The Correct Option is B

When light passes from one medium to another (like from water to air), it bends due to the difference in refractive indices. This effect is known as refraction. The apparent depth \( d' \) seen when looking at the bottom of the tank is related to the real depth \( d \) and the refractive index \( \mu \) by the formula: \[ d' = \frac{d}{\mu} \] Where:
\( d = 2 \, \text{m} \) (real depth),
\( \mu = \frac{4}{3} \) (refractive index of water).
Substituting the values: \[ d' = \frac{2}{\frac{4}{3}} = 2 \times \frac{3}{4} = 1.5 \, \text{m} \]

The correct option is (B): 1.5 m