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reason for dispersion of light using fermat principle..

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|dw:1350653499281:dw| had the interface not been there in between, lets say light, with velocity c, in time t, would have travelled a distance d = ct now there is dispersion, speed of V or v_v is less that v_r (red light) according to fermat's principle, the time taken is same for each to reach the same plane. now lets consider a plane (which i shall include in my next diagram) parallel to while light one. red light we all know has a greater speed, thus in same time, it'll travel a greater distance as compared to violet ,, but owing to fermat principle, they reach the plane together, hence, they deviate from their path in such a way to do that.. if they had moved on the same path, violet would have lagged behind, which fails fermat's principle..
what i want to ask through all this is that,, can above be treated as a satisfactory enough reason for dispersion ?

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one reason ofcorse i know is snells law, including velocity and angles..i just want to know if this one can be a reason ?
It's certainly related. Fermat's principle (as well as I can understand it) is due to destructive interference of waves, and the photons' interactions with electrons. Higher frequency light interacts more frequently and is refracted more.
well i dont know that much to be frank! :P in layman language ? can this thing be a reason for the bending of light ?
Light bends because higher frequencies (shorter wavelengths), i.e colors on the blue side of the spectrum, interact more with matter and are slowed down more.
and so as to follow fermat;s principle, red bends less and reaches to the same plane by travelling a greater dist, and vice versa for violet ?
It's not necessarily that they travel greater or less distance, but rather they spend more or less time in 'slow' regions. The light path is determined by which atoms cause the greatest constructive interference.
slow reigons ?
Yeah, I'm not sure how else to explain it.
mm.. nevermind,,thank you sir :)

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