Given that, the velocity of light in quartz = $1.5\times {10}^8\mathrm{m} {\mathrm{s}}^{-1}$ and velocity of light in glycerine = $\frac{9}{4}\times {10}^8\mathrm{m} {\mathrm{s}}^{-1}$. 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
 

• Correct answer
  A

  $6 \mathrm{cm}$
• B

  $3.55 \mathrm{cm}$
• C

  $9 \mathrm{cm}$
• D

  $2 \mathrm{cm}$

Solution

 

$\mathrm{n}=\frac{\mathrm{velocity} \mathrm{of} \mathrm{light} \mathrm{in} \mathrm{vaccum}}{\mathrm{velocity} \mathrm{of} \mathrm{light} \mathrm{in} \mathrm{medium}}$ ,

velocity of light in vacuum = $3\times {10}^8\mathrm{m} {\mathrm{s}}^{-1}$

${\text{n}}_{\text{quartz}}=2 {\text{; n}}_{\text{glycerine}}=\frac{4}{3}\Rightarrow \frac{{\text{n}}_{\text{quartz}}}{{\text{n}}_{\text{glycerine}}}=\frac{2}{4/3}=\frac{3}{2}={\mu }_{\text{rel}}$

$\text{shift}=\text{t}\left(1-\frac{1}{{\mu }_{\text{rel}}}\right)=18\left(-\frac{1}{3/2}\right)=6cm$

Hence, the correct answer is option: 'A'.