A fish in water (refractive index n ) looks at a bird vertically above in the air. If y is the height of the bird and x is the depth of the fish from the surface, then the distance of the bird as estimated by the fish is

Step-by-step solution

Refractive index of water =n Since, fish looks the bird from water (denser medium) to air (rarer medium). Hence, normal shift d=(n-1) h But according to question, real depth h=y d=(n-1) y ( height of bird =y) (i) The bird's height from the surface of the water is equal to the summation of the normal shift and height of the bird from the surface. i.e. d^ =y+d=y+ n-1) y [From Eq. (i)] d^ =n y Total actual distance between bird and fish =x+d^ =x+n y