Question

A plano convex lens ($\mu =1.5$) has a maximum thickness of $1mm$. If diameter of its aperture is $4cm$. Find (i) Radius of curvature of curved surface, (ii) its focal length in air

Answer 1

See the figure, A is a plano convex lens of thickness 1mm and diameter of its aperture is 4cm or 40mm.

So, AB=radius of aperture =20mm

AC =PC= radius of curvature =R

$BC=\left(R-1\right)mm$

Use pythagoras theorem,

$\begin{array}{c}A{C}^2=A{B}^2+B{C}^2\\ R^2={20}^2+{\left(R-1\right)}^2\\ R^2=400+R^2+1-2R\\ 401-2R=0\\ R=200.5mm\\ R_1=R=200mm\\ R_2=\infty \\ wkt,\\ \frac{1}{f}=\left(\mu -1\right)\left(\frac{1}{R_1}-\frac{1}{R_2}\right)=\left(1.5-1\right)\left(\frac{1}{200.5}-\frac{1}{\infty }\right)=\frac{1}{401}\end{array}$