Question

The image of an object, formed by a plano-convex lens at a distance of $8\,m$ behind the lens, is real and 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. 2 m
• C. 3 m
• D. 4 m

Answer 1

Answer: (C)

$\mu=\frac{\lambda_{ a }}{\lambda_{ m }}=\frac{3}{2}$
$\Rightarrow \frac{1}{ f }=\frac{\mu-1}{ R }=\frac{1}{2 R }$
$\Rightarrow \frac{1}{ f }=\frac{1}{ v }-\frac{1}{ u }$
$\Rightarrow \frac{1}{8}-\frac{1}{-24}=\frac{1}{2 R }$
$\Rightarrow \frac{3+1}{24}=\frac{1}{2 R }$
$\Rightarrow R =3 \,m$