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}$