Effective Refractive Index - Should be simple

In summary, the conversation discusses finding the effective refractive index, N, for a dielectric made of alternating layers with widths A and B and refractive indices (a*) and (b*). The speaker suggests using the equation c/n = wavelength x frequency = phase speed to find the total time taken for the wave to propagate through the distance A+B. However, this leads to the wrong value for N. The correct equation is N^2= [A(a*)^2 + B(b*)^2]/(A+B), where the optical path length, refractive index x physical length, must be used in the calculations.
  • #1
nathangrand
40
0
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?
 
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  • #2
Is it that I need to use the optical path length..ie refractive index x physical length in my calculations? That will make it work I think but can someone explain why...
 

FAQ: Effective Refractive Index - Should be simple

1. What is the effective refractive index?

The effective refractive index is a measure of how light travels through a medium, taking into account both the material's refractive index and its physical structure.

2. How is the effective refractive index calculated?

The effective refractive index is calculated using the following formula: neff = (nm2 * Vm + nair2 * Vair)1/2, where nm and nair are the refractive indices of the material and air, respectively, and Vm and Vair are the volume fractions of the material and air in the medium.

3. Why is the effective refractive index important?

The effective refractive index is important because it affects how light propagates through a material, and thus plays a crucial role in determining the performance of optical devices such as lenses, fibers, and waveguides.

4. How does the effective refractive index differ from the ordinary refractive index?

The ordinary refractive index only takes into account the material's refractive index, while the effective refractive index considers both the material's refractive index and its physical structure. This means that the effective refractive index can vary depending on the material's physical properties, such as its composition, temperature, and pressure.

5. Can the effective refractive index be negative?

Yes, the effective refractive index can be negative, which means that light is travelling in the opposite direction of the incident light. This phenomenon, known as negative refraction, has been demonstrated in certain artificial materials called metamaterials, and has potential applications in imaging, cloaking, and superlenses.

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