Double slit experiment wavelength

If the path length difference is (m+1/2)\lambda then you have destructive interference assuming the waves are out of phase.In summary, the question is about finding the equation for double slit interference and determining the distances of the first zero of irradiance and the fifth bright fringe from the principal axis. The path length difference between the two waves originating from the slits is crucial in determining constructive or destructive interference.
  • #1
fluidistic
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Homework Statement


A extent ray of light with wavelength [tex]\lambda _0=632.8 nm[/tex] incide over a screen containing 2 horizontal parallel slits very thin and separated by a distance of 0.2 mm. We observe an interferance over a screen at 1.00 meter away from the screen containing the horizontal slits.
1)At what distance from the principal axis are situated the first zeros of irradiance?
2)How far from the principal axis is the fifth bright fringe?
3)Compare the previous results.

Homework Equations


I know I should find the formula given there: http://en.wikipedia.org/wiki/Double-slit_experiment#Results_observed but how to reach this?

The Attempt at a Solution


3) Since I already made the experiment, I know that the fifth fringe is roughly 5 times farer than the 1st fringe, from the principal axis. Hmm not sure it's true, but I know that the distance between the fringes is equal. So my statement is true only if the first fringe coincide with the principal axis, which isn't true.
1)Irradiance is the Poynting vector averaged over... well I'm not sure. It's worth [tex]\frac{|\vec E_0 |^2}{2 \eta}[/tex] according to my notes. So I need to find out the electric field of the wave.
I know that there are 2 sources of light considering the problem after the light from the laser passed by the slits. How are these waves? Cylindrical? I never dealt with such waevs. Spherical? Can I consider them as plane waves since the 1 meter distance is really big compared to the wavelength of the wave? In that case E total is the sum of [tex]E_1= E_0 \cos (kx - \omega t + \alpha)[/tex] and [tex]E_2= E_0 \cos (k... - \omega t + \alpha)[/tex]. Can you help me with the "..." part? I don't know what to put as "x".

Also I don't know how can L=1m appear in the final result. I guess I should consider the wave as cylindrical, but I've no idea about how the expression is.
Any idea?
 
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  • #2
I don't understand a lot of what you are saying. But if all you need to do is find the double slit interference equation then all you need to do is find the path length difference between the two waves originating from both slits to the wall, [itex]\Delta L[/itex]. If the path length difference is [itex]m\lambda[/itex] then you have constructive interference assuming both waves are in phase.
 

1. What is the double slit experiment?

The double slit experiment is a classic physics experiment that demonstrates the wave-like nature of light. It involves shining a single beam of light through two parallel slits and observing the resulting interference pattern on a screen.

2. How is wavelength related to the double slit experiment?

The wavelength of light is a key factor in the double slit experiment. The distance between the slits and the resulting interference pattern on the screen corresponds to the wavelength of the light being used.

3. What happens when the wavelength is changed in the double slit experiment?

When the wavelength is changed, the resulting interference pattern on the screen will also change. A shorter wavelength will result in a narrower interference pattern, while a longer wavelength will result in a wider interference pattern.

4. Can the double slit experiment be performed with other types of waves besides light?

Yes, the double slit experiment can be performed with any type of wave, including sound waves and water waves. The key factor is the wavelength of the wave being used.

5. What is the significance of the double slit experiment in physics?

The double slit experiment is significant because it helped to prove the wave-particle duality theory, which states that particles can exhibit both wave-like and particle-like behavior. It also has implications in quantum mechanics and our understanding of the fundamental nature of reality.

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