Question

A plano-convex lens has diameter $5\,cm$ and its thickness at the centre is $0.25\,cm$ . If the speed of light inside the lens is $2\times 10^{8}\,ms^{- 1}$ , then if the focal length (in $cm$ ) of the lens is $\frac{2525}{x}$ then find $x$ .

Answer 1

R. I. of lens,
$\mu=\frac{c}{v}=\frac{3 \times 10^8}{2 \times 10^8}=\frac{3}{2}$
From $\triangle ACO$, radius of curvature of lens is,
$ R ^2= R _1^2+( R -0.25)^2$
$\therefore R ^2=(2.5)^2+( R -0.25)^2 $
$\therefore R ^2=6.25+ R ^2+0.0625-0.5 R $
$\therefore 0.5 R =6.3125 $
$\therefore R =12.625\, cm $
$ F =\frac{ R }{\mu-1}=\frac{12.625}{\frac{3}{2}-1}=25.25\, cm =\frac{2525}{100} cm$