A ray in moving from point A in space to point B in space takes path of least time or more exactly path of stationary time. Now a cylinder is made of a transparent material, but the refractive index of this material slowly decreases with increasing distance r from its axis according to the law $n=n\left(r\right)$ That is, the refractive index, is cylindrically symmetric. In the List I different refractive index expressions are given. Now a flash of light is made at some distance $\rho (\rho \ne 0)$ from the axis of cylinder such that some of the rays move along a circle centred on the cylinder axis. The possible value of $\rho$ are given in list II. Match the possible values of $\rho$ with the corresponding refractive index in List I. Here $n_o$ and $\gamma$ are known constants Only single option correct, so choose the most general answer.

 

	LIST I		LIST II
A	$n\left(r\right)=n_0(1-\gamma r)$	P	$\infty >\rho >0$
B	$n\left(r\right)=n_0(1-\gamma r^2)$	Q	$\rho =\sqrt{\gamma }$
C	$n\left(r\right)=n_0(1+\frac{\gamma }{r^2})$ for r>0	R	$\rho =\frac{1}{\sqrt{3\gamma }}$
D	$n\left(r\right)=\frac{n_0}{r}$ for r > 0	S	$\rho =\frac{1}{\sqrt{2\gamma }}$
		T	$\rho =\frac{1}{2\gamma }$