Question

The power of biconvex lens is 10 dioptre and the radius of curvature of each surface is 10 cm. Then the refractive index of the material of the lens is

• A. $\frac{3}{2}$
• B. $\frac{4}{3}$
• C. $\frac{9}{8}$
• D. $\frac{5}{3}$

Answer 1

Answer: (A)

$\frac{3}{2}$

Answer 2

Power of lens,
$P { (in\, dioptre)= \frac{100}{focal \, length \, f (in \, cm)}}$
$\therefore \:\:\:\: f = \frac{100}{10} = { 10 \, cm}$
According to lens maker?s formula
$\frac{1}{f} = (\mu -1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right)$
For biconvex lens, $R_1 = + R, R_2 = - R$
$\therefore \:\: \frac{1}{f}=\left(\mu-1\right)\left(\frac{1}{R} - \frac{1}{R}\right)$
$\frac{1}{f}=\left(\mu-1\right)\left(\frac{2}{R}\right)$
$\frac{1}{10}=\left(\mu-1\right)\left(\frac{2}{10}\right)$
$\left(\mu-1\right)=\frac{1}{2} \Rightarrow \mu=\frac{1}{2}+1=\frac{3}{2}$