A double convex lens has power P and same rad | vedclass

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(D) For a double convex lens, the radii of curvature are $R_1 = R$ and $R_2 = -R$. Using the lens maker's formula, the power $P$ is given by:$P = (\mu

Vedclass · Accepted Answer

$0.33$

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(D) For a double convex lens, the radii of curvature are $R_1 = R$ and $R_2 = -R$. Using the lens maker's formula, the power $P$ is given by:$P = (\mu - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right) = (\mu - 1) \left( \frac{1}{R} - \frac{1}{-R} \right) = (\mu - 1) \left( \frac{2}{R} \right) \quad ...(i)$For a plano-convex lens, the radii of curvature are $R_1' = R'$ and $R_2' = \infty$. The power $P'$ is given by:$P' = (\mu - 1) \left( \frac{1}{R'} - \frac{1}{\infty} \right) = (\mu - 1) \left( \frac{1}{R'} \right) \quad ...(ii)$Given that $P' = 1.5P = \frac{3}{2}P$, we substitute the expressions from $(i)$ and $(ii)$:$(\mu - 1) \left( \frac{1}{R'} \right) = \frac{3}{2} \left[ (\mu - 1) \left( \frac{2}{R} \right) \right]$$\frac{1}{R'} = \frac{3}{R}$Therefore, $R' = \frac{R}{3} \approx 0.33R$.

$A$ 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 $1.5P$ is ......$R$.

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