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Express the group velocity of light in t...

Express the group velocity of light in terms of the velocity of light in a vacuum, the refractive index and the derivative of the refractive index with respect to frequency .

Text Solution

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The correct Answer is:
`U= (c )/( n + omega (d n))/( d omega ))`
According to the definition, the group velocity is `U=lim_(Deltak to 0) (Deltaomega)/(Deltak) =(d omega)/(d k) = 1/((dk)/(domega))`
But the wave number is `k = omega/u=(n omega)/c` Differentiating, we obtain `(dk)/(domega)=n/c+omega/c(dn)/(domega)=1/c(n+omega (dn)/(d omega))`
Hence `U=c/(n+ omega (dn)/(d omega))`
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