# GRIN

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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