Question

An equi-concave lens is to be made of crown glass. What should be radii of the surfaces of the lens if the power of the lens is $-2.5$ dioptre and refractive index of crown glass is $1.65$?

• A. $52m$
• B. $62cm$
• C. $52cm$
• D. $520cm$

Answer 1

The correct option is C $52cm$

$\begin{array}{c}\text{Given power of lens}=-2.5D\\ \text{Power of lens}=\frac{100}{f\left(cm\right)}\\ \text{where}f=\text{focal length of the lens}\\ \text{so}-2.5=\frac{100}{f}\\ \begin{array}{cc}f& =-\frac{100}{25}\\ f& =-40cm\end{array}\end{array}$

Refractive index of lens $=1.65$

equi-concave lens having radius $=R$

$\frac{1}{f}=(\mu -1)(\frac{1}{R_1}-\frac{1}{R_2})$

$\frac{-1}{40}=\left(1.65\right)(\frac{1}{-R}-\frac{1}{R})$

$\begin{array}{cc}\frac{1}{40}& =\frac{\left(0.65\right)2}{R}\\ R& =40\left(0.65\right)2.\\ R& =52cm\end{array}$

so option $c$ is correct