Question

If in a plano-convex lens, radius of curvature of convex surface is $10\text{cm}$ and the focal length of lens is $30\text{cm}$, the refractive index of the material of the lens will be

• A. $1.5$
• B. $1.66$
• C. $1.33$
• D. $3$

Answer 1

The correct option is C $1.33$


Focal length of a plano - convex lens is given by
$$f=\frac{R_2}{\mu -1}\because [R_1=\infty ]$$
Substituting the data given in the question we get,

$30=\frac{10}{\mu -1}\Rightarrow \mu -1=\frac{1}{3}$

$\Rightarrow \mu =\frac{4}{3}\text{or}1.33$

Hence, option (c) is the correct answer.