Imagine a dielectric made of of alternating layers of widths A and B and refractive indices (a*) and (b*). Find the effective refractive index, N
So in general: c/n = wavelength x frequency = phase speed
My thinking was find the total time taken for the wave to propagate through the distance A+B and work out the refractive index from this.
So,
Time=distance/speed = (A+B)/(c/N) = (A/(c/a*)) +(B/(c/b*))
But this gives me the wrong value for N
The answer I'm looking for is N^2= [A(a*)^2 + B(b*)^2]/(A+B)
Where am I going wrong?
So in general: c/n = wavelength x frequency = phase speed
My thinking was find the total time taken for the wave to propagate through the distance A+B and work out the refractive index from this.
So,
Time=distance/speed = (A+B)/(c/N) = (A/(c/a*)) +(B/(c/b*))
But this gives me the wrong value for N
The answer I'm looking for is N^2= [A(a*)^2 + B(b*)^2]/(A+B)
Where am I going wrong?