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…

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