Question

The focal length of a plano - convex lens is equal to its radius of curvature of convex side. The value of the refractive index of its material is

• A. $1.33$
• B. $1.6$
• C. $1.5$
• D. $2$

Answer 1

The correct option is D $2$


For a plano - convex lens,

Radius of curvature of plane surface, $R_1=\infty$
Radius of curvature of curved convex surface, $R_2=-R\text{cm}$

From the data given in the question,

Focal length of lens, $f=R$

From lens maker's formula,

$\frac{1}{f}=(\mu -1)(\frac{1}{R_1}-\frac{1}{R_2})$

$\Rightarrow$$\frac{1}{f}=(\mu -1)(\frac{1}{\infty }-\frac{1}{-R})$

$\Rightarrow$$\frac{1}{R}=(\mu -1)\frac{1}{R}\because [f=R]$

$\therefore \mu =2$

Hence, option (d) is the correct answer.