Question

A beaker containing liquid is placed on a table, underneath a microscope which can be moved along a vertical scale. The microscope is focussed, through the liquid onto a mark on the table when the reading on the scale is a. It is next focussed 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. $\frac{d-a}{d-c-b+a}$
• B. $\frac{b-d}{d-c-b+a}$
• C. $\frac{d-c-b+a}{d-b}$
• D. $\frac{d-b}{a+-c-d}$

Answer 1

The correct option is A $\frac{d-a}{d-c-b+a}$

The real depth $=\mu$ (apparent depth)
$\Rightarrow$ In first case, the real depth $h_1=\mu (b-a)$
Similarly in thr second case, the real depth $h_2=\mu (d-c)$
since $h_2>h_1,$ the difference of real depths $=h_2-h_1=\mu (d-c-b+a)$
Since the liquid is added in second case, $h_2-h_1=(d-b)\Rightarrow \mu =\frac{(d-b)}{(d-c-b+a)}$