Question

The image of an object, formed by a plano-convex lens at a distance of 8 m behind the leens, is real is one third the size of the object. The wavelength of light inside the lens is $\frac{2}{3}$ times the wavelength in free space. The radius of the curved surface of the lens is

• A. 1 m
• B. 6 m
• C. 3 m
• D. 2 m

Answer 1

The correct option is C 3 m

$\mu =\frac{c}{v}=\frac{f{\lambda }_{air}}{f{\lambda }_{med}}=\frac{3}{2}\text{Now,}v=+8m,m=\frac{-1}{3}=\frac{v}{u}\Rightarrow u=-24m\frac{1}{f}=\frac{1}{v}-\frac{1}{u}\frac{1}{f}=\frac{1}{8}+\frac{1}{24}=\frac{4}{24}f=6mf=\frac{R}{\mu -1}6=\frac{R}{0.5}\Rightarrow R=3m$