Question

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

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

Answer 1

Answer: (B)

30 cm

The lens is as shown in the figure.

To determine the radius of curvature $R$ of the curved surface, we can write

$R^2=3^2+(R-\frac{3}{10}{)}^2$

Solving this, we get

$R=15.15cm$

Speed of light in any medium is $\frac{c}{\mu }$ where $c=3\times {10}^{8}m/s$ and $\mu$ is the refractive index.

For the lens, $\frac{c}{\mu }=2\times {10}^{8}m/s$

$\mu =\frac{3\times {10}^8}{2\times {10}^8}=1.5$

Putting these values in the lens makers formula for plano convex lens, we have,

$\frac{1}{f}=(\mu -1)\left(\frac{1}{R}\right)=(1.5-1)\left(\frac{1}{15.15}\right)c{m}^{-1}$

Solving this, we get $f\approx 30cm$