Each quarter of a vessel of depth `H` is filled with liquids of the refractive indices `n_(1),n_(2), n_(3)` and `n_(4)` from the bottom respectively. The apparent depth of the vessel when looked normally is

Options

A. `(H(n_(1)+n_(2)+n_(3)+n_(4)))/(4)`
B. `(H((1)/(n_(1))+(1)/(n_(2))+(1)/(n_(3))+(1)/(n_(4))))/(4)`
C. `((n_(1)+n_(2)+n_(3)+n_(4)))/(4H)`
D. `(h((1)/(n_(1))+(1)/(n_(2))+(1)/(n_(3))+(1)/(n_(4))))/(2)`

Answer

B

Explanation

Apparent depth of bottom
`=(H//4)/(mu_(1))+(H//4)/(mu_(2))+(H//4)/(mu_(3))+(H//4)/(mu_(4))`
`=(H)/(4)((1)/(u_(1))+(1)/(mu_(2))+(1)/(mu_(3))+(1)/(mu_(4)))`