Question

Diameter of a plano–convex lens is 6 cm and thickness at the centre is 3 mm. If the speed of light in the material of the lens is 2 10⁸ m/sec, the focal length of the lens is

• A. 15 cm
• B. 20 cm
• C. 30 cm
• D. 10 cm

Answer 1

The correct option is C 30 cm

According to lens formula $\frac{1}{f}=(\mu -1)[\frac{1}{R_1}-\frac{1}{R_2}]$
The lens is plano-convex i.e., $R_1=R$ and $R_2=\infty$
Hence $\frac{1}{f}=\frac{\mu -1}{R}\Rightarrow f=\frac{R}{\mu -1}$
Speed of light in medium of lens $v=2\times {10}^{8}m/s$
$\Rightarrow \mu =\frac{c}{v}=\frac{3\times {10}^8}{2\times {10}^8}=\frac{3}{2}=1.5$

If r is the radius and y is the thickness of lens (at the centre), the radius of curvature R of its curved surface in accordance with the figure is given by
$R^2=r^2+(R-y{)}^2\Rightarrow r^2-y^2-2Ry=0$
Neglecting $y^2$; we get $R=\frac{r^2}{2y}=\frac{(\frac{6}{2}{)}^2}{2\times 0.3}=15cm$
Hence $f=\frac{15}{1.5-1}=30cm$