A vessel of depth d is half filled with liquid of refractive index `mu_1`, and half filled with liquid of refractive index `mu_2`. Bottom will be at depth ..... when viewed from top and perpendicularly to surface.

Options

A. `2d(mu_2)/(mu_1)`
B. `2d mu_1mu_2`
C. `d/2[(1)/(mu_1)+(1)/(mu_2)]`
D. `2d[(1)/(mu_1)+(1)/(mu_2)]`

Answer

A, B, C, D

Explanation

`(h_i)/(h_0)=(1)/(mu_2)`
`therefore h_i=(h_0)/(mu_2)=(d)/(mu_2)`
and `(h._i)/(h._0)=(1)/(mu_1)`
`therefore h._i=(h_i^1)/(mu_1)=(d)/(mu_2)`
Viewed depth of bottom,
`h_i+h._i=d/mu_2+d/mu_1=d[1/mu_1+1/mu_2]`