Question

37. What will be the dispersion for the wavelength 21 if for a wavelength 1 the dispersion of the medium is D?​

Answer 1

Answer:

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Answer 2

The dispersion of a medium for wavelength λ is D. Then the dispersion for the wavelength 2λ will be:

• The wavelength or wavenumber of a wave is related to its frequency by a dispersion relation. The phase velocity and group velocity of waves in the medium may be calculated as a function of frequency using the dispersion relation.
• When pure plane waves of various wavelengths propagate at different speeds, dispersion occurs, causing a wave packet of mixed wavelengths to spread out in space.

Cauchy's Dispersion formula is as follows:

μ= A+ B/ λ2

And dispersion

D= -   dλ

       ------  

        dμ

​

As a result of the two equations above:

D = −(−2λ3) B= 2B/ λ3  

This suggests that

D α1/ λ3

 Hence,

D'/D  = (  λ /  λ'  ) ³

 

As λ  ′ =2λ

Therefore,

D  ′  =D/8