MCQ
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
  • $\frac{{d - b}}{{d - c - b + a}}$
  • B
    $\frac{{b - d}}{{d - c - b + a}}$
  • C
    $\frac{{d - c - b + a}}{{d - b}}$
  • D
    $\frac{{d - b}}{{a + b - c - d}}$

Answer

Correct option: A.
$\frac{{d - b}}{{d - c - b + a}}$
a
(a) The real depth $ = \mu $ ( apparent depth)

$ \Rightarrow $ In first case, the real depth ${h_1} = \mu (b - a)$

Similarly in the 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)}}$

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