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 $1.5P$ is:

• A. $\frac{R}{2}$
• B. $2R$
• C. $\frac{3R}{2}$
• D. $\frac{R}{3}$

Answer 1

Answer: (D)

$R_1=R_2=R$
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)

$P^{\prime }=\frac{1}{f^{\prime }}=\left({\mu }_t-1\right)\left(\frac{1}{R^{\prime }}\right)$ ___(ii)
$P^{\prime }=\frac{3}{2}P$
$\left({\mu }_{\ell }-1\right)\left(\frac{1}{R^{\prime }}\right)=\mu \frac{3}{2}\left({\mu }_{\ell }-1\right)\left(\frac{2}{R}\right)$
$\therefore R^{\prime }=\frac{R}{3}$