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  4. A double convex lens has power P and same radii of curvature R of both the surfaces. The radius of curvature of a surface of a plano- convex lens made of the same material with power 1.5 P is:

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Q. A double convex lens has power $P$ and same radii of curvature $R$ of both the surfaces. The radius of curvature of a surface of a plano- convex lens made of the same material with power $1.5 \,P$ is:

JEE MainJEE Main 2020Ray Optics and Optical Instruments

Solution:

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$R _{1}= R _{2}= R$
Power (P)
Refractive index is assume $\left(\mu_{f}\right)$
$P =\frac{1}{ f }=\left(\mu_{t}-1\right)\left(\frac{2}{ R }\right)$ ____(i)
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$P ^{\prime}=\frac{1}{ f ^{\prime}}=\left(\mu_{t}-1\right)\left(\frac{1}{ R ^{\prime}}\right)$ ___(ii)
$P^{\prime}=\frac{3}{2} P$
$\left(\mu_{\ell}-1\right)\left(\frac{1}{R^{\prime}}\right)=\mu \frac{3}{2}\left(\mu_{\ell}-1\right)\left(\frac{2}{R}\right)$
$\therefore R^{\prime}=\frac{R}{3}$