Question

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
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 1

The real depth `=(R.I.)`(apparent depth)
`rArr` In first case, the real depth `h_(1)=n(b-a)`
Similarly, in the second case, the real depth `h_(2)=n(d-c)`
Since, `h_(2) gt h_(1)` the difference of real depths `=h_(2)-h_(1)=n(d-c-b+a)`
Since the liquid is added in second case, `h_(2)-h_(1)=d-b`
`rArr n=(d-b)/(d-c-b+a)`