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  4. Radii of curvature of a converging lens are in the ratio 1: 2. Its focal length is 6 cm and refractive index is 1.5. Then its radii of curvature are

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Q. Radii of curvature of a converging lens are in the ratio $1 : 2$. Its focal length is $6 \,cm$ and refractive index is $1.5$. Then its radii of curvature are

KCETKCET 2013Ray Optics and Optical Instruments

Solution:

Given, $\frac{R_{1}}{R_{2}}=\frac{1}{2}, f=6 \,cm$ and $\mu=1.5$
Let $R_{1}=R$ and $R_{2}=2 R$
We know the focal length of converging lens
By using relation $\frac{1}{f}=(\mu-1)\left[\frac{1}{R_{1}}+\frac{1}{R_{2}}\right]$
Substituting all the values, we get $R=4.5\, cm$
$\therefore R_{1}=4.5 \,cm$ and $R_{2}=2 \times 4.5=9 \,cm$