A laser beam propagates through a spherically symmetric medium.The refractive index varies with diatance to the symmetry centre C by the law mu=mu'(r/ro) where mu'=1,ro=3cm
ro

Question

A laser beam propagates through a spherically symmetric medium.The refractive index varies with diatance to the symmetry centre C by the law mu=mu'(r/ro) where mu'=1,ro=3cm 
ro<=r<infinity. The beam's trajectory lies in the plane that includes C.At distance r1=8√2cm the beam makes an angle 30°with the normal at that surface.Find the minimum distance the beam reach relative to symmetry centre C.

irishboy123 · Answer

post/ scan the original question.  this looks interesting.

samigupta8 · Answer

This is the original question.

irishboy123 · Answer

this is a standard problem in Calculus of Variations.  That is how I would do it.  

If that is what you are looking to study, I can get the ball rolling later.  Not sure whet the process will spit out, sometimes it's really horrible, sometimes a breeze.

If there is another approach, soz, right now fraid i can't think of it.

samigupta8 · Answer

Would you like to hVe a look at my way ?

irishboy123 · Answer

yes that would be very interesting

just attach it here maybe?

samigupta8 · Answer

Won't be able to do that (attachement)!
I can describe it though.
We know that the product of refractive index and angle of incidence is always a constant quantity so i used it here.
So by that i got mu1sin30°=mu2sin90°
(Sin90° bcoz we want minimum distance from symmetry centre)
From here i found the value of distance (minimum) becoz we have been given the variation of mu with the distance from symmetry centre.

irishboy123 · Answer

that doesn't sound right to me, but it does sound incredibly inventive.

hope it worked!

samigupta8 · Answer

Can u please point out the mistake in this if there is one?
I really do wanna know the fault here.

irishboy123 · Answer

|dw:1460988945837:dw|

i think i see what you did.  that is brilliant!!

samigupta8 · Answer

But the biggest problem is that it's not the ans .
Ans is 8 and i got 4√2 .
:(

irishboy123 · Answer

the CoV approach gives 8.  i will latex and attach as pdf for ref when i get chance, buts its just a load of maths gobble-de-gook.  [and of course i could have goofed]

i wonder if your approach coupled with some calculus might give an intuitive insight into this?  might try that later.

irishboy123 · Answer

CoV approach attached

of limited interest i know....just for completeness

samigupta8 · Answer

Never heard of that before.
Whatever it is ,we might get some help from ganeshie sir though.

irishboy123 · Answer

good idea!

samigupta8 · Answer

@ganeshie8