Consider a cylindrical optical fiber with a core that has a graded index (GRIN) of refraction given by \[ n(r)=n_{0}\sqrt{1- (g r)^2}\] where \(r\) is the distance to from the optical axis of the fiber. Show that this profile results in continual refocusing of paraxial rays as shown in the figure below. If \( g=0.33~\mbox{mm}^{-1}\), determine the distance \(d\) in millimeters between two consecutive focal points.

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