In the following I am always talking about fraunhoffer diffraction(adsbygoogle = window.adsbygoogle || []).push({});

suppose you have two slits in a doulbe slit diffraction experiment which are both exposed to the same plane wave (say the same laser) as the original source of radiation. Usually, we expect that both slits will act as EQUAL sources of radiation to the extent that they produce a diffraction pattern on a distant screen. the Irradiance of this diffraction pattern is given by

I = I(0)(sin(B)/B)^2*cos(A)^2

where B = 1/2bksin(theta)

A = 1/2aksin(theta)

where b = slit width

a = centre to centre slit speration

theta = anglular position on the screen

BUT now suppose we change the situation so that the second slit has a film over it that prevents complete transmission. say only a fraction c of the radiation is transmitted through c. Then we have to rework the derivation of the double slit diffraction.

QUESTION:

1) I have come accross the following equation for the situation above with the second slit transmitting only a fraction c of the radiation that it would normally transmit (and which the first slit DOES transmit)

I = I(0)/K*(sin(B)/B)^2*(1+c^2+2c[cos(2A)])

where K is a constant.

HOW DO YOU DERIVE THIS EQUATION?????????????

I have been trying to derive this equation from integrating of the apperture as usual, but including the factor c in the second integral (ie multiplying it), but I simply cannot work it out. Can you either refer me to somewhere where this derivation might be set out? or set it out for me? I have tried and tried for hours, and I get something kind of close, but never manage to get it in this form? please help!!!

2) also, just a question about the sort of diffraction effect that would result from this situation: should you expect the intensity pattern on the screen to be symetrical still? I guess I could thing about the mathematics and make a conclusion, but could you explain physically?

3)If this situation were changed so that we were in teh Fresnel (near-slit) regime? would it be symmetric of asymmetric? again, could you explain physically? I'm not too familiar with Fresnel diffraction (of course I know what it is, but I haven't actually done any Fresnel analysis ever) so could you explain physically as best you can?

Thanks a lot.

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# Double-slit diffraction with UNEQUAL source amplitude

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