Question

a spherical convex surface separates object and image spaces of refractive indices 1.00 and 4/3 respectively. if the radius of curvature is 10 cm, find focus of the convex surface?​

Answer 1

refractive index of convex lens , $\mu_2=4/3$

using formula ,

$\frac{\mu_2}{v}-\frac{\mu_1}{u}=\frac{\mu_2-\mu_1}{R}$

where , v = focal length = f [ we assume that parallel rays converges at focus so, image position = focal length , f ]

u = ∞

so, $\frac{4/3}{f}-\frac{1}{\infty}=\frac{4/3-1}{R}$

given, radius of curvature, R = 10cm

so $\frac{4}{3f}=\frac{1}{3\times10}$

or, $\frac{4}{3f}=\frac{1}{30cm}$

or, $f=40cm$

hence, focus of the convex lens is 40cm