A vesse of depth x is half filled with oil of refractive index `mu_(1)` and the other half is filled with water of refrative index `mu_(2)`. The apparent depth of the vessel when viewed above is

Options

A. `(x(mu_(1)+mu_(2)))/(2mu_(1)mu_(2))`
B. `(xmu_(1)mu_(2))/(2(mu_(1)+mu_(2)))`
C. `(xmu_(1)mu_(2))/((mu_(1)+mu_(2)))`
D. `(2x(mu_(1)+mu_(2)))/(mu_(1)mu_(2)`

Answer

A

Explanation

As, refractive index, `mu=(Real depth)/(Apparent depth)`

`:.` Apparent depth of the vessel when viewed from above is `d(apparent)=(x)/(2mu_(1))+(x)/(2mu_(2))=(x)/(2)((1)/(mu_(1))+(1)/(mu_(2)))`
`=(x)/(2)((mu_(2)+mu_(1))/(mu_(1)mu_(2)))=(x(mu_(1)+mu_(2)))/(2mu_(1)mu_(2))`