# Fringe Pattern Brightness for Young's Double-slit experiment

Perhaps I have missed something in my notes, but I have noticed when looking at different sources that some textbooks/sites state that the fringe brightness for the young's experiment is the same for all the bright fringes. Others, say that the brightness "falls off" with angle theta. Well, which is it? And how do you calculate it, not using derivatives if possible... I'm preparing for the MCAT exam and calculus is not tested. Thanks!

Here are some pictures that I've come across either in different textbooks or websites:

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Please provide references and links for all the sources you quote. –  Emilio Pisanty Jul 29 '14 at 20:25
The brightness will be equal if you consider the effect of interference only. But the brightness will fall off if take into account the phenomena diffraction along with interference. –  noir1993 Jul 30 '14 at 7:09
To explain the theta dependence you have to derive the diffraction integral which requires calculus. –  noir1993 Jul 30 '14 at 7:11
Thanks noir... got it. The textbooks have an interesting way of presenting topics without being clear about about what is merely theoretical vs what is observed. –  hau5junkie87 Jul 30 '14 at 20:11

The Intenisty distribution of a double slit diffraction is $$I=I_0\cos^2[\frac{\pi d \sin(\theta)}{\lambda}]$$ Where we define $\tan(\theta)=\frac{\Delta y}{L}$. Remember that the y spacing is proportional to the slit seperation so we end up that $$\tan\theta\approx \frac{d}{L}$$ In the one figure, it is stated that L>>d, so we use the approximation that $sin\theta=\theta$, so that equation for I above would have no angular dependance in that case.