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A Young experiment is set up using a continuous laser source of monochromatic plane waves with wavelength λ, an opaque barrier with two equal size vertical slits and a sliding light detector that can produce an irradiance graph for all of the light passing through the slits. The width of each slit (b) and the separation distance between the central axes of the two slits (a) are all safely larger than λ. All of these (λ, a and b) are each safely smaller in scale than the distance between the laser and the barrier with slits and also smaller than the distance between the barrier with slits and the track of the sliding light detector. This jointly means that a fraunhofer analysis of the setup should yield a valid forecast of the irradiance graph produced.

A derivation of the irradiance distribution yields this formula:

I(θ) = 4I_{0}(cos^{2}α)(sin^{2}β/β^{2})

where

θ is the angle that a position of the sliding detector makes with the center point between the slits,

I(θ) is the irradiance at a position of the sliding detector represented by angle θ,

I_{0}is what one would expect for the irradiance at the position directly opposite one slit in a setup with just one of the two slits, if that one slit were positioned directly between the laser and the detector,

α is the difference in waves between light from one slit and light from the other slit, given by πasinθ/λ,

β is the difference in waves between light from one edge of a slit and light from the other edge of that slit, given by πbsinθ/λ,

(and to repeat,) a is the separation distance between the centers of the two slits and b is the width of each slit.

This irradiance distribution formula for a fraunhofer analysis is given in two references.

Eugene Hecht,Optics 4th ed.,Addison Wesley(2002)

Grant Fowles,Introduction to Modern Optics wnd ed.,Dover(1975)

(slight but insignificant difference in notation due to differences in defining I_{0})

QUESTION

What would be the computed prediction of the integrated and averaged irradiance over the range of the detector, based on this setup and the irradiance distribution formula?

I assume that a computer and software capable of producing a Young irradiance graph would also be able to sum it and compute a mean value. The authors of the two references don't do this and I don't know how to figure the answer.

(thx to hydr0matic for the idea!)

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# Total energy through a Young experiment

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