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

Options

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

Answer

A

Explanation

Apparent depth `= ("real depth")/(mu)`
For oil apparent depth `= (x)/(2 mu_(1))`
and for water apparent depth `= (x)/(2mu_(2))`
The apparent depth of the vessel
`= (x)/(2mu_(1)) + (x)/(2 mu_(2))`
`=(x)/(2)[(1)/(mu_(1)) + (1)/(mu_(2))] = (x)/(2)[(mu_(1) + mu_(2))/(mu_(1) mu_(2))]`