Question

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

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

Answer 1

The correct option is C $30cm$

According to lens formula $\frac{1}{f}=(\mu -1)[\frac{1}{R_1}-\frac{1}{R_2}]$
The lens 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, 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 $y^2;weget$R=\dfrac {r^2}{2y}=\dfrac {(6/2)^2}{2\times 0.3}=15\ cm$
Hence $f=\frac{15}{1.5-1}=30cm$