A vessel of depth 2d cm is half filled with a liquid of refractive index `mu_(1)` and the upper half with a liquid of refractive index `mu_(2)`. The apparent depth of the vessel seen perpendicularly is

Options

A. `(d)/(2)[(1)/(mu_(1))+(1)/(mu_(2))]`
B. `2d[(1)/(mu_(1))+(1)/(mu_(2))]`
C. `d[(1)/(mu_(1))+(1)/(mu_(2))]`
D. `(2)/(d)[(1)/(mu_(1))+(1)/(mu_(2))]`

Answer

C

Explanation

Apparent depth= `("Real depth")/(mu)`
For `1` st liquid, Apparent depth= `(d)/(mu_(1))`
For `2` nd liquid, Apparent depth= `(d)/(mu_(2))`
`:.` Total apparent depth= `(d)/(mu_(1))+(d)/(mu_(2))=d[(1)/(mu_(1))+(1)/(mu_(2))]`