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Q.
The thickness at the centre of a plano convex lens is $3 mm$ and the diameter is $6 cm$. If the speed of light in the material of the lens is $2 \times 10^{8} ms ^{-1}$. The focal length of the lens is
JEE MainJEE Main 2021Ray Optics and Optical Instruments
Solution:
$R ^{2}= r ^{2}+( R - t )^{2}$
$R ^{2}= r ^{2}+ R ^{2}+ t ^{2}-2 Rt$
Neglecting $t ^{2}$, we get
$R =\frac{ r ^{2}}{2 t }$
$\therefore \frac{1}{ f }=(\mu-1)\left(\frac{1}{ R }-\frac{1}{\infty}\right)=\frac{\mu-1}{ R }$
$f =\frac{ R }{\mu-1}=\frac{ r ^{2}}{2 t (\mu-1)}=\frac{\left(3 \times 10^{-2}\right)^{2}}{2 \times 3 \times 10^{-3} \times\left(\frac{3}{2}-1\right)}$
$=\frac{9 \times 10^{-4}}{6 \times 10^{-3} \times 1} \times 2$
$f =0.3 \,m =30\, cm$
