Question

Given that, the velocity of light in quartz = $1.5\times 10^{8}m{s}^{-1}$ and velocity of light in glycerine = $\frac{9}{4}\times 10^{8}m{s}^{-1}$ . If a slab made of quartz is placed in front of an object kept in glycerine (as shown in the figure), then the shift of the object produced by slab is

• A. $6cm$
• B. $3.55cm$
• C. $9cm$
• D. $2cm$

Answer 1

Answer: (A)

$n=\frac{\text{ velocity of light in vaccum }}{\text{ velocity of light in medium }}$
velocity of light in vacuum $=3\times 10^{8}m{s}^{-1}$
$n_{\text{quartz }}=2;n_{\text{glycerine }}=\frac{4}{3}\Rightarrow \frac{n_{\text{quartz }}}{n_{\text{gliccrinc }}}=\frac{2}{4/3}=\frac{3}{2}={\mu }_{rel}$
shift $=t\left(1-\frac{1}{{\mu }_{rel}}\right)=18\left(-\frac{1}{3/2}\right)=6cm$