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  4. The figure shows an equiconvex lens of focal length f. If the lens is cut along PQ, the focal length of each half will be

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Q. The figure shows an equiconvex lens of focal length $ f. $ If the lens is cut along PQ, the focal length of each half will bePhysics Question Image

Bihar CECEBihar CECE 2010Ray Optics and Optical Instruments

Solution:

According to Lens Makers formula,
$ \frac{1}{f}=(\mu -1)\left( \frac{1}{R}-\frac{1}{R} \right) $
$ \Rightarrow $ $ \frac{1}{f}=(\mu -1)\left( \frac{2}{R} \right) $ ..... (i)
On cutting, $ \frac{1}{f}=(\mu -1)\left( \frac{1}{R}-\frac{1}{\infty } \right) $
$ \frac{1}{f}=(\mu -1)\left( \frac{1}{R} \right) $ ..... (ii)
From Eqs. (i) and (ii), we get
$ f=2f $