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  4. The radius of curvature of the convex face of a planoconvex lens is 15 cm and the refractive index of the material is 1.4 . Then the power of the lens in dioptre is

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Q. The radius of curvature of the convex face of a planoconvex lens is $ 15 \,cm $ and the refractive index of the material is $ 1.4 $ . Then the power of the lens in dioptre is

KEAMKEAM 2008Ray Optics and Optical Instruments

Solution:

$ \frac{1}{f}(\mu -1)\left( \frac{1}{{{R}_{1}}}-\frac{1}{{{R}_{2}}} \right) $
For planoconvex lens $ {{R}_{1}}=\infty ,{{R}_{2}}=-R=-1.5\,cm,\mu =1.4 $
$ \therefore $ $ \frac{1}{f}=(1.4-1)\left( 0+\frac{1}{15} \right) $
or $ \frac{1}{f}=0.4\times \frac{1}{15} $
Therefore, power of the lens in diopter
$ P=\frac{100}{f}=\frac{40}{15}=2.66D $