Question

Diameter of a plano-convex lens is $5\, cm$ and thickness at the centre is $0.25\, cm$. 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

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