Question

A beaker contains water up to a height h₁​ and kerosene of height h₂​ above water, so that the total height of (water + kerosene) is (h₁ ​+ h₂​). Refractive index of water is μ₁​ and that of kerosene is μ₂​. The apparent shift in the position of the bottom of the beaker when viewed from above is ______.

Options

• `(1-1/mu_1)"h"_2+(1-1/mu_2)"h"_1`

• `(1+1/mu_1)"h"_1+(1+1/mu_2)"h"_2`

• `(1-1/mu_1)"h"_1+(1-1/mu_2)"h"_2`

• `(1+1/mu_1)"h"_2-(1+1/mu_2)"h"_1`

Answer 1

A beaker contains water up to a height h₁​ and kerosene of height h₂​ above water, so that the total height of (water + kerosene) is (h₁ ​+ h₂​). Refractive index of water is μ₁​ and that of kerosene is μ₂​. The apparent shift in the position of the bottom of the beaker when viewed from above is `underlinebb((1-1/mu_1)"h"_1+(1-1/mu_2)"h"_2)`.

Explanation:

The apparent shift in the bottom of the beaker will be equal to the sum of the individual shifts caused by the kerosene and water mediums.

Shift because of water = h₁`(1-1/mu_1)`

Shift because of kerosene = h₂`(1-1/mu_2)` 

Hence, the net shift  will be, `"h"_1(1-1/mu_1)+"h"_2(1-1/mu_2)`