# Wave optics of reflection

1. Aug 11, 2004

### niko2000

Hi,
Right now I am solving some exercises in connection with wave optics. If we have three layers of different materials (ex. air, gasoline, water) and we send a light ray through these layers and we calculate the wave length of the reflected rays, then we use these formulas:
D = N*l; (D = optical distance, l = wave length)
If the ray reflects from the material with greater n, then we must D replace with D+l/2....
I am a little bit confused about my knowledge of these things.
I don't have any problems with exercises, but I would like to understand the theory a little bit better
Could anyone comment the meaning of N and relations between the rays reflected from the surface and bottom of the second layer?
Is it possible that ray passes through the third layer?

2. Aug 11, 2004

I think you have to learn more about thin films and interference. Have you learned this or no? the $$\frac{D+1}{2}$$ has to do with the number of dark or light fringes you see.

3. Aug 11, 2004

### Claude Bile

The Optical Path Length is different to the physical path length. In a high refractive index material, light is slowed down more and must therefore undergo more cycles than if it were travelling in a vacuum. OPL is primarily used when comparing the phases of two or more rays (as you are doing here, essentially).

The OPL (or D as you have called it is given by);

D = n*L where L is the physical distance the light travels through the layer.

Now, the wavelengths with the highest reflectivities are the wavelengths that constructively interfere with one another, that is the ray reflected off the first surface and the ray reflected off the second surface must be in phase.

In order for this condition to be met, the optical path length of the light travelling through the extra layer must be an integer multiple of the wavelength.

This is the origin of the equation D = N*l. N in this case is simply a positive integer.

The reason you must sometimes replace D with D+l/2 is because light reflecting off a material with a greater refractive index undergoes a 90 degree phase shift. This effectively increases the OPL by have a wavelength (Recall that OPL is a measure of phase rather than physical distance).

And yes, it is entirely possible for rays to pass through the third layer.

Claude.