A laser beam propagates through a region whose refractive index varies as \(\mu = \mu_0 (\frac{r}{r_0})\). At a distance of R the beam makes an angle of 30 degrees with the normal.

Find the minimum separation between the beam and the center of this region(the point where \(r=0\)) in cm.

Assume \(\mu_0= 1\), \(r_0= 3 \text{cm}\), \(R= 8\sqrt2\text{ cm} \).

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