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  4. Consider a bi-convex lens and a plano-convex lens, with radii of curvature of all the curved surfaces being same. If f is the focal length of bi-convex lens then, the focal length of the plano-convex lens is

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Q. Consider a bi-convex lens and a plano-convex lens, with radii of curvature of all the curved surfaces being same. If $f$ is the focal length of bi-convex lens then, the focal length of the plano-convex lens is

J & K CETJ & K CET 2015Ray Optics and Optical Instruments

Solution:

Consider the type of lenses shown below:
For bi- Plano convex lens, focal length is given by
$\frac{1}{f_{b}}=(\mu-1)\left(\frac{1}{R}+\frac{1}{R}\right)=\frac{2(\mu-1)}{R}$
For plano-convex lens focal length is given by
$\frac{1}{f_{b}}=(\mu-1)\left(\frac{1}{R}+\frac{1}{R}\right)$
$=\frac{(\mu-1)}{R}$
$\Rightarrow \frac{f_{b}}{f_{p}}=\frac{\frac{R}{2(\mu-1)}}{\frac{R}{(\mu-1)}}$
$=\frac{1=2 f_{b}}{2}$
$\Rightarrow f_{p}=2 f$

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