A double convex lens has power

Question:

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:

  1. $\frac{\mathrm{R}}{2}$

  2. $2 \mathrm{R}$

  3. $\frac{3 R}{2}$

  4. $\frac{\mathrm{R}}{3}$


Correct Option: , 4

Solution:

$\mathrm{R}_{1}=\mathrm{R}_{2}=\mathrm{R}$

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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