Question

The image of an object placed in air formed by a convex refracting surface is at a distance of $10m$ behind the surface. The image is real and is at $\frac{2^{rd}}{3}$ of the distance of the object from the surface .The wavelength of light inside the surface is $\frac{2}{3}$ times the wavelength in air. The radius of the curved surface is $\frac{x}{13}m.$ the value of 'x' is _________.

Answer 1

Answer: 30

${\lambda }_m=\frac{{\lambda }_a}{\mu }\Rightarrow \mu =\frac{3}{2}$
$\frac{\mu }{v}-\frac{1}{u}=\frac{\mu -1}{R}$
$\frac{3}{2\times 10}+\frac{1}{15}=\frac{\frac{3}{2}-1}{R}$
$R=\frac{30}{13}$
$=30$