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. 6 m

Answer 1

Answer: (C)

3 m

$Refractiveindex,\mu =\frac{{\lambda }_a}{{\lambda }_m}=\frac{3}{2}$
$m=\frac{v}{u}$. Or $u=m\times v=3\times 8=24$

$\Rightarrow \frac{1}{f}=\frac{\mu -1}{R}=\frac{1}{2R}$

$\Rightarrow \frac{1}{f}=\frac{1}{v}-\frac{1}{u}$

$\Rightarrow \frac{1}{8}-\frac{1}{-24}=\frac{1}{2R}$

$\Rightarrow \frac{3+1}{24}=\frac{1}{2R}$

$\Rightarrow R=3m$