Question

The image of an object placed in air formed by a convex refracting surface is at a distance of $10\,m$ 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

$\lambda_{ m }=\frac{\lambda_{ a }}{\mu} \Rightarrow \mu=\frac{3}{2}$
$\frac{\mu}{ v }-\frac{1}{ u }=\frac{\mu-1}{ R }$
$\frac{3}{2 \times 10}+\frac{1}{15}=\frac{\frac{3}{2}-1}{ R }$
$R =\frac{30}{13}$
$=30$