Question 224 of 295

The thickness at the centre of a plano convex lens is $3mm$ and the diameter is $6cm.$ 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 ___________.

A$0.30cm$B$15cm$C$1.5cm$D$30cm$

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Answer: (D) $30cm$

${R}^{2}={r}^{2}+(R-t{)}^{2}$
${R}^{2}={r}^{2}+{R}^{2}+{t}^{2}-2Rt$
Neglecting ${t}^{2},$ we get
$R=\dfrac{{r}^{2}}{2t}$
$∴\dfrac{1}{f}=\left(\mu -1\right)\left(\dfrac{1}{R}-\dfrac{1}{\infty }\right)=\dfrac{\mu -1}{R}$
$f=\dfrac{R}{\mu -1}=\dfrac{{r}^{2}}{2t(\mu -1)}=\dfrac{{\left(3\times {10}^{-2}\right)}^{2}}{2\times 3\times {10}^{-3}\times \left(\dfrac{3}{2}-1\right)}$
$=\dfrac{9\times {10}^{-4}}{6\times {10}^{-3}\times 1}\times 2$
$f=0.3m=30cm$