Question

When a biconvex lens of glass having refractive index $1.47$ is dipped in a liquid, it acts as a plane sheet of glass. This implies that the liquid must have refractive index

• A. Greater than that of glass
• B. Less than that of glass
• C. Equal to that of glass
• D. Less than one

Answer 1

The correct option is C Equal to that of glass

The given biconvex lens is acting as a plane glass sheet, then the focal length of the combination of lens and liquid becomes infinity.
$\Rightarrow f=\infty$
Applying lens maker's formula,
$\frac{1}{f}=(\frac{{\mu }_2}{{\mu }_1}-1)(\frac{1}{R_1}-\frac{1}{R_2})$
or, $\frac{1}{f}=(\frac{{\mu }_g}{{\mu }_l}-1)(\frac{1}{R_1}-\frac{1}{R_2})$
For a biconvex lens, $R_1=+R,R_2=-R$


or, $\frac{1}{f}=\left(\frac{{\mu }_g-{\mu }_l}{{\mu }_l}\right)\left(\frac{2}{R}\right)$
$\Rightarrow \frac{1}{\infty }=\frac{{\mu }_g-{\mu }_l}{{\mu }_l}.\frac{2}{R}$
or, $\frac{2({\mu }_g-{\mu }_l)}{{\mu }_l.R}=0$
$\therefore {\mu }_g={\mu }_l$
$\Rightarrow {\mu }_l=1.47$
$$\begin{array}{c}\text{Why this question ?}\\ \text{Bottom line : If the refractive index of lens and surrounding medium}\text{is same, then light}\text{wouldn't suffer refraction.}\end{array}$$