Question

Focal length of the plano-convex lens is _____ when its radius of curvature of the surface is $R$ and $n$ is the refractive index of the lens

• A. $f=R$
• B. $f=R/2$
• C. $f=R/(n-1)$
• D. $f=(n-1)/R$

Answer 1

The correct option is C $f=R/(n-1)$

Figure shows a plano-convex lens of refractive index $\mu =n$.

From Lens Maker's formula:-

$\frac{1}{f}=(\frac{{\mu }_2}{{\mu }_1}-1)(\frac{1}{R_1}-\frac{1}{R_2})$

where, ${\mu }_2$ and ${\mu }_1$ are refractive index of lens and surrounding medium respectively.

And, $R_1$ and $R_2$ are radius of 1st and 2nd surfaces respectively.

Here,

${\mu }_1=1,{\mu }_2=n,R_1=-\infty ,R_2=-R,f=2R$

Hence,

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

$⟹\frac{1}{f}=(n-1)\frac{1}{R}$

$⟹f=\frac{R}{n-1}$

Answer-(C)