1. The problem statement, all variables and given/known data
If light moves from a medium with a refractive index that is a function of wavelength, [\itex]n_1(\lambda)[/itex], to vacuum [itex]n_2=1[/itex], then dispersion will occur. Find the incident angle [itex]\theta_1[/itex] that will maximize dispersion.
3. The attempt at a solution
I'm interpreting 'maximum dispersion' as if we change the wavelength a little, then the angle of refraction [itex]\theta_2[/itex] should change a lot. So I think we trying to find the maximum of the function [itex]\frac{d\theta_2}{d\lambda}[/itex], which means solving [itex]\frac{d^2\theta_2}{d\lambda^2}=0[/itex] for [itex]\theta_1[/itex].
Is the correction interpretation and approach? Thanks
If light moves from a medium with a refractive index that is a function of wavelength, [\itex]n_1(\lambda)[/itex], to vacuum [itex]n_2=1[/itex], then dispersion will occur. Find the incident angle [itex]\theta_1[/itex] that will maximize dispersion.
3. The attempt at a solution
I'm interpreting 'maximum dispersion' as if we change the wavelength a little, then the angle of refraction [itex]\theta_2[/itex] should change a lot. So I think we trying to find the maximum of the function [itex]\frac{d\theta_2}{d\lambda}[/itex], which means solving [itex]\frac{d^2\theta_2}{d\lambda^2}=0[/itex] for [itex]\theta_1[/itex].
Is the correction interpretation and approach? Thanks
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