Question 208 of 295

Diameter of a plano - convex lens is $6cm$ and thickness at the centre is $3mm$. If the speed of light in the material of lens is $2\times 1{0}^{8}m{s}^{-1}$, the focal length of the lens is:

A$30cm$B$10cm$C$15cm$D$20cm$

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Answer: (A) $30cm$

$AB=6cm$

$r=3cm$
$O{A}^{2}=O{P}^{2}+P{A}^{2}$

${R}^{2}={\left(R-t\right)}^{2}+{r}^{2}$

${R}^{2}={R}^{2}+{t}^{2}-2Rt+{r}^{2}$

$2Rt={t}^{2}+{r}^{2}$

$R=\dfrac{{t}^{2}+{r}^{2}}{2t}=\dfrac{{\left(0\cdot 3\right)}^{2}+{\left(3\right)}^{2}}{2\times 0\cdot 3}$

$R\approx \dfrac{ {r}^{2}}{2t}=\dfrac{{\left(3\right)}^{2}}{2\times 0\cdot 3}=\dfrac{9}{0\cdot 6}=\dfrac{90}{6}=15cm$

Use $\dfrac{1}{f}=\left(\mu -1\right)\left(\dfrac{1}{{R}_{1}}-\dfrac{1}{{R}_{2}}\right)$

$\dfrac{1}{f}=\left(1\text{.}5-1\right)\left(\dfrac{1}{15}\right)=\dfrac{1}{30}$

$f=30cm$

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