A beaker contains water up to a height `h_(1)` and kerosene of height `h_(2)` above water so that the total height of (water + kerosene) is `(h_(1) + h_(2))` . Refractive index of water is `mu_(1)` and that of kerosene is `mu_(2)` . The apparent shift in the position of the bottom of the beaker when viewed from above is :-

Options

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

Answer

B

Explanation

Actual depth `=(h_(1)+h_(2))`
Shift of bottom due to water
`d_(1)=h_(1)-(h_(1))/(mu_(1)))`
`=(1-(1)/(mu_(1))h_(1)`
Shift of bottom due to kerosene
`d_(2)=(h_(2)-(h_(2))/(mu_(2)))=h_(2)(1-(1)/(mu_(2)))`
Combined shift of bottom when viewed from above
Total shift `=d_(1)+d_(2)`
Apparent shift in the position
`h_(2)=(1-(1)/(mu_(1)))+h_(2)(1-(1)/(mu_(2)))`