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. equal to that of glass
• B. less than one
• C. greater than that of glass
• D. less than that of glass

Answer 1

Answer: (A)

According to lens maker's formula
$\frac{1}{f}=\left(\frac{{\mu }_g}{{\mu }_L}-1\right)\left(\frac{1}{R_1}-\frac{1}{R_2}\right)$
where ${\mu }_g$ is the refractive index of the material of the lens and ${\mu }_L$ is the refractive index of the liquid in which lens is dipped.
As the biconvex lens dipped in a liquid acts as a plane sheet of glass, therefore
$f=\infty \Rightarrow \frac{1}{f}=0$
$\therefore \frac{{\mu }_g}{{\mu }_L}-1=0$
or ${\mu }_g={\mu }_L$