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  4. A double convex lens has focal length 25 cm. 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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Q. A double convex lens has focal length 25 cm. 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 :

NEETNEET 2019Ray Optics and Optical Instruments

Solution:

$\frac{1}{f} = \left(\frac{\mu_{2} -\mu_{1}}{\mu_{1}}\right)\left(\frac{1}{R_{1}} - \frac{1}{R_{2}}\right) $
$ \Rightarrow \frac{1}{25} = \left(\frac{1.5 -1}{1}\right)\left(\frac{1}{R} -\frac{1}{\left(-2R\right)}\right) $
$ \Rightarrow \frac{2}{25} = \frac{3}{2R} $
$ \Rightarrow R = \frac{75}{4} = 18.75$