Question

A traveling microscope is focused on to a point on the bottom of a vessel. A liquid whose refractive index is $\frac{6}{5}$ is poured in it. The microscope is lifted to 6 cm to focus it again. The depth of the liquid in the vessel is

• A. 7.2cm
• B. 36cm
• C. 9cm
• D. 24cm

Answer 1

Answer: (A)

7.2cm

$\begin{array}{c}f=f\\ f^{\prime }=f+6-\left(i\right)\\ \mu =\frac{6}{5}\end{array}$

$\text{let vessel depth be `d`}$

$\begin{array}{c}d=f-\left(i\right)\\ d_{\text{apparent}}=f^{\prime }\text{(iii)}\\ \text{from (i) and (iii)}\end{array}$

$\begin{array}{c}{d}_{\text{apparent}}=f+6\\ d(1+\frac{1}{\mu })=f+6-\left(iv\right)\end{array}$

$\text{from}\left(ii\right)\text{and}\left(iv\right)$

$\begin{array}{cc}d(1+\frac{1}{6/5})& =d+6\\ d+\frac{5d}{6}& =d+6\\ 5d& =36\\ d& =7.2cm\end{array}$