Question

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 $ z $ is the depth of the fish from the surface, then the distance of the bird as estimated by the fish is

• A. \( x + y \left(1 - \frac{1}{n}\right) \)
• B. \( x + ny \)
• C. \( x + y \left(1 + \frac{1}{n}\right) \)
• D. \( y + z \left(1 - \frac{1}{n}\right) \)

Hint:

When considering refraction, remember that the apparent distance of an object in a medium with refractive index \( n \) is given by \( n \times \text{real distance} \). This formula is crucial for solving problems involving refraction at boundaries.

Answer 1

The Correct Option is B

When a fish looks at a bird in air, the bird appears to be at a different position due to the refraction of light. The distance between the fish and the bird is affected by the refractive index \( n \) of water. - The true distance of the bird from the fish is \( y \). - The fish sees the bird at an apparent distance due to refraction at the water surface. According to the law of refraction and apparent depth formula, the fish perceives the height of the bird to be stretched by a factor of the refractive index. The apparent distance \( x \) of the bird as perceived by the fish is given by: \[ x = y \cdot n \]
Thus, the total perceived distance of the bird as estimated by the fish is: \[ x + ny \]
Thus, the correct answer is: \[ \text{(B) } x + ny \]