Question

To a bird in air, a fish in water appears to be at 30 cm from the surface. If refractive index of water with respect to air is \(\frac {4}{3}\) ,the real distance of bird from the surface is

• A. 30 cm
• B. 50 cm
• C. 40 cm
• D. 60 cm

Answer 1

The Correct Option is C

Snell's law: 
n = \(\frac {d}{d'}\) 
In this case, the refractive index of water with respect to air is given as \(\frac {4}{3}\). We are given that the fish appears to be at a depth of 30 cm from the surface (d'). We need to find the real depth (d) of the bird. 
Applying Snell's law: 
\(\frac {4}{3}\) = \(\frac {d}{30}\)
d = \(\frac {4}{3}\) x 30 
d = 40 cm 
Therefore, the correct answer is (C) 40 cm.

Answer 2

Given:
The apparent depth of the fish from the bird's perspective, \(d' = 30\) cm
The refractive index of water n with respect to air is \(\frac{4}{3}\)
Let:
Real depth of the fish from the water surface, d (which is what we need to find).
Distance of the bird from the water surface, x.
According to the laws of refraction, the relationship between the real depth d, apparent depth d', refractive index n, and the distance between the observer and the interface x is given by:
\(\frac{d'}{d} = \frac{1}{n}\)

\(\frac{30 \text{ cm}}{d} = \frac{1}{\frac{4}{3}}\)

\(\frac{30 \text{ cm}}{d} = \frac{3}{4}\)

Cross-multiplying to solve for d:
\(30 \cdot \frac{4}{3} = d\)
\(d = 40 \text{ cm}\)

So, the correct answer is (C): 40 cm.