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 $1.5 \mathrm{P}$ is:
Correct Option: , 4
$\mathrm{R}_{1}=\mathrm{R}_{2}=\mathrm{R}$
Power (P)
Refractive index is assume $\left(\mu_{\ell}\right)$
$\mathrm{P}=\frac{1}{\mathrm{f}}=\left(\mu_{\ell}-1\right)\left(\frac{2}{\mathrm{R}}\right)$..(1)
$\mathrm{P}^{\prime}=\frac{1}{\mathrm{f}^{\prime}}=\left(\mu_{\ell}-1\right)\left(\frac{1}{\mathrm{R}^{\prime}}\right)$..(2)
$\mathrm{P}^{\prime}=\frac{3}{2} \mathrm{P}$
$\left(\mu_{\ell}-1\right)\left(\frac{1}{R^{\prime}}\right)=\mu \frac{3}{2}\left(\mu_{\ell}-1\right)\left(\frac{2}{R}\right)$
$\therefore \quad \mathrm{R}^{\prime}=\frac{\mathrm{R}}{3}$
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