A beaker containing liquid is placed on a table, underneath a microscope which can be moved along a vertical scale. The microscope is focused, through the liquid onto a mark on the table when the reading on the scale is `a`. It is next focused on the upper surface of the liquid and the reading is `b`. More liquid is added and the observations are repeated, the corresponding readings are `c` and `d`. The refractive index of the liquid is

Options

A. `(d - b)/(d - c - b + a )`
B. `(b -d )/(d -c - b + a)`
C. `(d - c - b + a)/(d - b)`
D. `(d - b )/(a + b - c -d)`

Answer

A

Explanation

Actual depth = `n xx d_(app)`
`h_(1) = n(b -a ) rarr ` 1st case
`h_(2) = n(d - c) rarr` 2nd case
Since, `h_(2) gt h_(1)`
`h_(2) - h_(1) = n (d -c -b + a)`
Since, the liquid is added in `2^(nd)` case
`h_(2) - h_(1) = d- b `
`therefore " " n = ( (d - b)/(d - c - b + a))`