JEE MAIN - Physics (2013 (Offline) - No. 11)
Diameter of a plano-convex lens is $$6$$ $$cm$$ and thickness at the center is $$3mm$$. If speed of light in material of lens is $$2 \times {10^8}\,m/s,$$ the focal length of the lens is
$$15$$ $$cm$$
$$20$$ $$cm$$
$$30$$ $$cm$$
$$10$$ $$cm$$
Explanation
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$$\therefore$$ $$n = {{Velocity\,\,of\,\,light\,\,in\,\,vacuum} \over {Velocity\,\,of\,\,light\,\,in\,\,medium}}$$
$$\therefore$$ $$n = {3 \over 2}$$
$${3^2} + {\left( {R - 3mm} \right)^2} = {R^2}$$
$$ \Rightarrow {3^2} + {R^2} - 2R\left( {3mm} \right) + {\left( {3mm} \right)^2} = {R^2}$$
$$ \Rightarrow R \approx 15\,cm$$
$${1 \over f} = \left( {{3 \over 2} - 1} \right)\left( {{1 \over {15}}} \right) \Rightarrow f = 30\,cm$$
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