A double convex lens has focal length 25cm. The radius of curvature of one of the surfaces is double of the other. Find the radii, if the refractive index of the material of the lens is 1.5.
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For the double convex lens
$f = 25cm, R_1= R$ and $R_2 = -2R$ (sign convention)
$\frac{1}{\text{f}}=(\mu-1)\Big(\frac{1}{\text{R}_1}-\frac{1}{\text{R}_2}\Big)$
$\Rightarrow\frac{1}{25}=(15-1)\Big(\frac{1}{\text{R}_1}-\frac{1}{-2\text{R}}\Big)=0.5\Big(\frac{3\text{R}}{2}\Big)$
$\Rightarrow\frac{1}{25}=\frac{3}{4}\frac{1}{\text{R}}\Rightarrow\text{R}=18.75\text{cm}$
$R_1= 18.75cm, R_2 = 2R = 37.5cm.$
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