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 $\frac{2^{\mathrm{rd}}}{3}$ of the distance of the object from the surface. The wavelength of light
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
Solution:
$(30)$
$\lambda_{\mathrm{m}}=\frac{\lambda_{\mathrm{a}}}{\mu} \Rightarrow \mu=\frac{3}{2}$
$\frac{\mu}{\mathrm{v}}-\frac{1}{\mathrm{u}}=\frac{\mu-1}{\mathrm{R}}$
$\frac{3}{2 \times 10}+\frac{1}{15}=\frac{\frac{3}{2}-1}{\mathrm{R}}$
$\mathrm{R}=\frac{30}{13}$
$=30$