Question

When a bi - convex 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

If two or more lenses are in contact, the equivalent focal length is given by the formula
$$\frac{1}{f}=\sum _{i=1}^n\frac{1}{f_i}$$
Here,
$$\frac{1}{f}=\frac{1}{f_1}+\frac{1}{f_2}+\frac{1}{f_3}......\left(1\right)$$
Focal length of an plano - concave lens is given by
$$f_1=-\frac{R}{{\mu }_1-1}$$
Where, ${\mu }_1$ is the refractive index of liquid and $R$ be the radius of curvature.

Focal length of an equi - convex lens is given by
$$f_2=\frac{R}{2({\mu }_2-1)}$$
From the data given in the question, $f_1=f_3$ and $f=\infty .$

From $\left(1\right)$,

$0=-\frac{{\mu }_1-1}{R}+\frac{2({\mu }_2-1)}{R}-\frac{{\mu }_1-1}{R}$

$\Rightarrow \frac{2({\mu }_2-{\mu }_1)}{R}=0$

$\Rightarrow {\mu }_1={\mu }_2$

But according to the question , ${\mu }_2=1.47$

$\therefore {\mu }_1=1.47$

Hence, option (c) is the correct answer.