Question

The diameter of aperture of a plano-convex lens is 6 cm and its maximum thickness is 3 mm. If the velocity of light in the material of the lens is $2\times {10}^{8}m/s$, its focal length is : (approximately)

• A. $10cm$
• B. $15cm$
• C. $30cm$
• D. $60cm$

Answer 1

The correct option is C $30cm$

Refractive index $\mu =\frac{c}{v}=\frac{3\times {10}^8}{2\times {10}^8}=\frac{3}{2}$

From the figure we have

$BE\times ED=AE\times CE$

$3\times 3=\left(R+R-0.3\right)\times 0.3$

$\frac{9}{0.3}=2R-0.3$

$30=2R-0.3$

$2R=30.3$

$R\simeq 15cm$

Hence, $\frac{1}{f}=\left(\mu -1\right)\left(\frac{1}{R_1}-\frac{1}{R_2}\right)$

$R_2$ is infinity since it is a plano convex lens.

$\frac{1}{f}=\left(1.5-1\right)\left(\frac{1}{15}-\frac{1}{\infty }\right)$

$\Rightarrow \frac{1}{f}=\frac{1}{2}\times \frac{1}{15}=\frac{1}{30}$

$\therefore f=30cm$

Hence the correct answer is option (C).