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

Answer

A

Explanation

The real depth = (R.l.) apparent depth
`implies` In first case, the real depth ht = n(b-a)
Similarly in the second case,- the real depth `h_(2)` =? n (d-c)
Since. `h_(2)` > h, the difference of real depths = `h_(2)` - hi = n (d-c-b+a).
Since the liquid is added in second case, `h_(2)` - h! = d-b
`impliesn=(d-b/(d-c-b+a))`
Hence (A) is correct.