Single Slit Diffraction Pattern

[mohdfasieh]

Hello ,

How r u .


i know the formula of SINGLE SLIT DIFFRACTION PATTERN but i don,t know the method ho to drive it.Can any GENIUS tell me the procedure to drive this equation.


DERIVATION starts in this manner:

let d the separation b/w any two consecutive slits,D=(N-1)
r1 is the distance of first slit to point P on screen and similarly r2 is the distance of second slit from P and so on,then electric field at point P due to contribution from all N slits will be

E=A(r)cos(kr1-wt)+A(r)cos(kr2-wt)+......A(r)cos(krn-wt)

can u tell me the next steps how to drive the equation


please please please do reply

 

[Nate810]

soon.The next step is to calculate the intensity of the light at the point P, which is given by the formula I=E^2/2R, where R is the resistance of the conductor and E is the electric field at the point P. From this equation, we can calculate the intensity of the light at point P due to diffraction pattern. We can also use the formula I=A cos^2 (kr1-wt) + A cos^2 (kr2-wt)+......A cos^2 (krn-wt), where A is the amplitude of the wave. Using these two equations, we can derive the equation for single slit diffraction pattern.

 

[thepatientmental]

Hello,

I am not sure what specific equation you are referring to for the single slit diffraction pattern, as there are a few different equations that can be used to describe this phenomenon. However, I can provide a general overview of the derivation process for the equation that describes the intensity of the diffraction pattern.

The first step is to consider a single slit with width a, through which a monochromatic light wave with wavelength λ is passing. We can then define the angle θ as the angle between the incident light wave and the normal to the slit. The next step is to consider a point P on the screen at a distance L from the slit, and we can define the distance from the center of the slit to this point as x.

Using Huygen's principle, we can consider the slit as a series of point sources, each producing a spherical wave. The superposition of these waves will result in a diffraction pattern on the screen. The amplitude of each of these waves can be calculated using the Huygen-Fresnel principle, and the resulting electric field at point P can be found by adding up the contributions from all the point sources. This will result in an equation similar to the one you have provided, with A(r) representing the amplitude of each point source and r representing the distance from the source to point P.

The next step is to use the small angle approximation sinθ ≈ θ, which is valid when the angle θ is small. This allows us to simplify the equation and express it in terms of the angle θ. We can then use the trigonometric identity sinθ ≈ θ to further simplify the equation and express it in terms of the width of the slit a and the distance to the screen L. This will result in an equation for the electric field at point P that is dependent on these variables, as well as the wavelength of the incident light and the amplitude of the point sources.

Finally, we can use the intensity of the electric field, which is proportional to the square of its amplitude, to derive the equation for the intensity of the diffraction pattern on the screen. This will result in an equation that describes the intensity as a function of the angle θ, the width of the slit a, the distance to the screen L, and the wavelength of the incident light λ.

I hope this helps to provide a general overview of the derivation process for the equation of the single slit diffraction