Question

Diameter of a plano-convex lens is $5cm$ and thickness at the centre is $0.25cm$. If speed of light in material of lens is $2.25\times 10^{8}m/s$, the focal length of the lens is _______ $cm$.

Answer 1

Answer: 37.88

R. I. of lens, $\mu =\frac{c}{V}=\frac{3\times 10^8}{2,25\times 10^8}=\frac{4}{3}$
From $△ACO$, radius of curvature of lens is,
$R^2=R_1^2+(R-0.25{)}^2$
$\therefore R^2=(2.5{)}^2+(R-0.25{)}^2$
$\therefore R^2=6.25+R^2+0.0625-0.5R$
$\therefore 0.5R=6.3125$
$\therefore R=12.625cm$.
$F=\frac{R}{\mu -1}=\frac{12.625}{\frac{4}{3}-1}$
$=37.875=37.8$
....(Rounding off to $2$ decimal places)