A breaker 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 _2 + ( 1 - ( 1) / ( mu _ 2 ) ) h _ 1 `
B. ` ( 1 + ( 1 )/ ( mu _ 1) ) h _ 1 + ( 1 + ( 1 ) / ( mu _ 2 )) h _ 2 `
C. ` ( 1 - ( 1 ) / ( mu _ 1 )) h _ 1 + ( 1 - ( 1 ) / ( mu _ 1 ) ) h _ 2 `
D. ` ( 1 + ( 1 ) / ( mu _ 1 ) ) h _ 2 - ( 1 + ( 1 ) / ( mu _ 2 ) ) h _ 1 `

Answer

C

Explanation

Apparent shift ` Delta h = ( 1 - ( 1 ) /( mu ) ) h`
Apparent shift produced by water
` Delta h _ 1 = ( 1- ( 1 )/( mu _ 1 ) ) h _ 1 `
and apparent shift produced by kerosene
` Delta h _ 2 = ( 1 - ( 1 ) /( mu _ 2 )) h _ 2 `
The apparent shift in the position of the botton of the beaker when viewed from the above and apparent shift produced by kerosene
` Delta h = Delta h _ 1 + Delta h _ 2 `
` Delta h = ( 1 - ( 1 )/( mu _ 1 )) h _ 1 + ( 1- ( 1 ) /( mu _ 2 ) ) h _ 2 `