Question

A double convex lens has two surfaces of equal radii R and refractive index $m=1·5$. We have,
(a) $f=R/2$
(b) $f=R$
(c) $f=-R$
(d) $f=2R$.

Answer 1

(b) f = R

As from lens maker formula:
$$\begin{gathered} \frac{1}{f}=(m-1)(\frac{1}{R_1}-\frac{1}{R_2}) \\ \Rightarrow \frac{1}{f}=(1.5-1)(\frac{1}{R}-\frac{1}{-R})(\mathrm{As}\mathrm{given}{R}_1=R_2=R) \\ \frac{1}{f}=(0.5)(\frac{1}{R}+\frac{1}{R}) \\ \frac{1}{f}=(0.5)\left(\frac{2}{R}\right) \\ f=R \end{gathered}$$=R