Question

A vessel of depth 2d cm is half filled with a liquid of refractive index μ₁ and the upper half with liquid of refractive index μ₂, the apparent depth as seen normally is ______.

Options

• `d[(mu_1mu_2)/(mu_1 + mu_2)]`

• `d[1/mu_1 + 1/mu_2]`

• `2d[1/mu_1 + 1/mu_2]`

• `(2d)/(mu_1mu_2)`

Answer 1

A vessel of depth 2d cm is half filled with a liquid of refractive index μ₁ and the upper half with liquid of refractive index μ₂, the apparent depth as seen normally is `underlinebb(d[1/mu_1 + 1/mu_2])`.

Explanation:

Since the refractive index of a medium can be given by,

`mu = "real depth"/"apparent depth"`

⇒ Apparent depth = `"Real depth"/mu`

∵ Total apparent depth = `d/mu_1 + d/mu_2 = d(1/mu_1 + 1/mu_2)`