Question

A bird in the air looks at a fish vertically below it and inside the water in a tank. If the distance of the fish as estimated by the bird is x₁ and that of the bird as estimated by the fish is x₂, then the refractive index of water is ______.

Options

• `x_1/x_2`

• `x_2/x_1`

• `(x_1 + x_2)/x_2`

• `(x_1 + x_2)/x_1`

Answer 1

A bird in the air looks at a fish vertically below it and inside the water in a tank. If the distance of the fish as estimated by the bird is x₁ and that of the bird as estimated by the fish is x₂, then the refractive index of water is `bbunderline(x_2/x_1)`.

Explanation:

The fish is in water, so it sees the bird in the air. The distance (x₂) estimated by the fish is the real height of the bird (in air). The bird sees the fish in the water and estimates the distance (x₁), which is the apparent depth of the fish underwater.

The refractive index of water, defined as the ratio of real depth to apparent depth, is:

∴ Refractive index = `x_2/x_1`

Here, (x₂) is the real distance (bird’s height) and (x₁) is the apparent distance (fish’s depth), so the refractive index is `x_2/x_1`.