Question:
The image of an object placed in air formed by a convex refracting surface is at a distance of $10 \mathrm{~m}$ behind the surface. The image is real and is at $\frac{2^{\text {rd }}}{3}$ 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 $\frac{x}{13} \mathrm{~m}$. the value of ' $x$ ' is
Solution:
$\lambda_{\mathrm{m}}=\frac{\lambda_{\mathrm{a}}}{\mu} \Rightarrow \mu=\frac{3}{2}$
$\frac{\mu}{v}-\frac{1}{u}=\frac{\mu-1}{R}$
$\frac{3}{2 \times 10}+\frac{1}{15}=\frac{\frac{3}{2}-1}{R}$
$\mathrm{R}=\frac{30}{13}$
$=30$