Question

The thickness at the centre of a plano convex lens is $3mm$ and the diameter is $6cm$. If the speed of light in the material of the lens is $2\times 10^{8}m{s}^{-1}$. The focal length of the lens is

• A. $0.30cm$
• B. $15cm$
• C. $1.5cm$
• D. $30cm$

Answer 1

Answer: (D)

$R^2=r^2+(R-t{)}^2$
$R^2=r^2+R^2+t^2-2Rt$
Neglecting $t^2$, we get
$R=\frac{r^2}{2t}$
$\therefore \frac{1}{f}=(\mu -1)\left(\frac{1}{R}-\frac{1}{\infty }\right)=\frac{\mu -1}{R}$
$f=\frac{R}{\mu -1}=\frac{r^2}{2t(\mu -1)}=\frac{{\left(3\times 10^{-2}\right)}^2}{2\times 3\times 10^{-3}\times \left(\frac{3}{2}-1\right)}$
$=\frac{9\times 10^{-4}}{6\times 10^{-3}\times 1}\times 2$
$f=0.3m=30cm$