Question

Diameter of a 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. $15\,cm$
• B. $20 \,cm$
• C. $30\, cm$
• D. $10\, cm$

Answer 1

Answer: (C)

$30\, cm$

Answer 2

By Pythagoras theorem
$\, \, \, \, \, \, \, \, \, R^2=(3)^2+(R-0.3)^2 \Rightarrow \, \, R \approx$ 15 cm
Refractive index of material of lens $\mu =\frac{c}{v}$
Here c = speed of light in vacuum = 3 x $10^8$ m/s
v = speed of light in material of lens = 2 x $10^8$ m/s
\hspace55mm =\frac{3 \times 10^8}{2 \times 10^8}=\frac{3}{2}
From lens maker's formula
\hspace25mm \frac{1}{f}=(\mu-1) \big(\frac{1}{R_1}-\frac{1}{R_2}\big)
Here, $R_1 = R \, and \, R_2 = \infty$ (For plane surface)
\hspace25mm \frac{1}{f}=\big(\frac{3}{2}-1\big) \big(\frac{1}{15}\big)
\Rightarrow \hspace25mm f=30 cm