# Interference of different lights

• Dimani4
In summary, two lasers of different wavelengths can produce interference when they are close together. This interference results in a different color being perceived.

#### Dimani4

Hi ppl,

I have a question to you. What happens if we approach two lasers with different wavelengths close together while they going in the same direction?
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did we get the interference between the different wave length of lasers result the different wavelength means different color?
as here: http://www.olympusmicro.com/primer/java/interference/index.html

what happens if we point these two lasers at one point? did we get the different color?

how close they should be to get the interference between them (minimum distance)?

thank you.

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This is interesting! I have frequently read that in dual slit type experiments that individual photons only interfere with themselves, while the posted link suggests this not true.

yes for me it was also interesting. 2day I've asked some ppl about that question and I think that the interference of the two photons from the different lasers with different wavelength is possible from the theoretic point of view but very complicated practically because of of coherence length of the lasers. when we speak about two lasers with different phases when we try to add their electric field and find out the electric flux that will carry this wave we get just the sums of the two intensities of each wave. like this:
E1=A1exp(i(w1t-k1x));
E2=A2exp(i(w2t-k2x-phase));

Etotal=E1+E2 and Itotal=I1+I2 (I1=A1^2;I2=A2^2)and there is no interference between the two waves. All we get it's just a higher intensity because more photons are in the region when the two lasers together.
But in the case of the two equal lasers with the same phase we get real the intereference in the energy flux equation, like

E1=A1exp(i(wt-kx))
E2=A2exp(i(wt-kx))

Etotal=(A1+A2)exp(i(wt-kx))

Itotal=A1^2+A2^2+A1XA2*+A2XA1*, so here we see the interference pattern (A1XA2*+A2XA1*) that actually play significant role in the increasing of the energy flux of the additive waves.

Actually to get two lasers with the same phases almost impossible. As I know in practice the laser can be splited into the two waves with the beam splitter and afterwards these two equal waves can be added (holography).

Dimani4 said:
Hi ppl,

I have a question to you. What happens if we approach two lasers with different wavelengths close together while they going in the same direction?
---------------->
-.-.-.-.-.-.-.-.-.>

did we get the interference between the different wave length of lasers result the different wavelength means different color?
You don't have a single wavelenght anylonger, so you have a wave, no more sinusoidal (I assume both lasers are monochromatic) which Fourier spectrum is given by the sum of two Dirac Delta functions located in two different points (the two lasers' wavelenghts).
The colour, intended as perception, changes in a very simple way, known from the theory of colours, the same which allows you to see a yellow spot in you PC monitor as given by the mixing of green and red pixels. Blue+red = violet/magenta, blue+green = cyan, red+yellow = orange, and so on.

lightarrow said:
You don't have a single wavelenght anylonger, so you have a wave, no more sinusoidal (I assume both lasers are monochromatic) which Fourier spectrum is given by the sum of two Dirac Delta functions located in two different points (the two lasers' wavelenghts).
The colour, intended as perception, changes in a very simple way, known from the theory of colours, the same which allows you to see a yellow spot in you PC monitor as given by the mixing of green and red pixels. Blue+red = violet/magenta, blue+green = cyan, red+yellow = orange, and so on.

thanx man. very clear explanation.