# GRIN

**Electricity and Magnetism**Level 3

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.