Question

A lean boy named Ramesh placed a glass slab of refractive index $\frac{3}{2}$ on his photograph. He felt it more interesting as his face appeared bigger than the original size when observed from the top of the glass slab. He also observed that the photo appears at a height of $1.5$ cm from the bottom. He then placed another glass cube made of different material and having the same thickness over the first glass cube. Now, he himself started to laugh by seeing his photograph as it appeared still bigger than the previous. When observed from the top the photograph appears to be at a height of $4$ cm from the bottom. Determine the refractive index of the second glass cube.

• A. $1.5$
• B. $2.25$
• C. $3.75$
• D. $1.75$

Answer 1

The correct option is B $2.25$

The vertical shift due to refractive index variation is given by
$\delta =t(\mu -1)$
here t is thickness of medium
$\mu$ is refractive index of medium.
and for this question it is given
${\delta }_1=1.5cm$ ${\mu }_1=\frac{3}{2}$
${\delta }_2=4cm$ for ${\mu }_2=8$
so
$\frac{{\delta }_1}{{\delta }_2}=\frac{t({\mu }_1-1)}{t({\mu }_2-2)}$
$\frac{1.5}{4}=\frac{\frac{3}{2}-1}{{\mu }_2-1}$
$\frac{3}{8}=\frac{1}{2({\mu }_2-1)}$
${\mu }_2-1=\frac{4}{3}$
${\mu }_2=\frac{7}{3}$