# A double convex lens has power P and same radii of curvature R of both the surfaces. The radius of curvature of surface of a plano-convex lens made of the same material with power 1.5 P is : Option: 1 $2R$   Option: 2 Option: 3   Option: 4

$\mathrm{R}_{1}=\mathrm{R}_{2}=\mathrm{R} \\ Power (P) \\ Refractive index is assume (\mu)$

$\mathrm{P}=\frac{1}{\mathrm{f}}=\left(\mu_{l}-1\right)\left(\frac{2}{\mathrm{R}}\right)$

\begin{aligned} &\mathrm{P}^{\prime}=\frac{1}{\mathrm{f}^{\prime}}=\left(\mu_{\ell}-1\right)\left(\frac{1}{\mathrm{R}^{\prime}}\right)\\ &P^{\prime}=\frac{3}{2} P \end{aligned}

$\begin{array}{l} \left(\mu_{\ell}-1\right)\left(\frac{1}{\mathrm{R}^{\prime}}\right)=\mu \frac{3}{2}\left(\mu_{\ell}-1\right)\left(\frac{2}{\mathrm{R}}\right) \\ \\ \therefore \quad \mathrm{R}^{\prime}=\frac{\mathrm{R}}{3} \end{array}$

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