Hi all. So let us say I shine a laser through a slit of width w, the distance to the screen is L, the distance from the center of the pattern formed to the first next bright fringe (next because the center is a bright fringe) is a. Using Fraunhofer diffraction.(adsbygoogle = window.adsbygoogle || []).push({});

Given variables: a, w and L

My book gives the equation for dark fringes. I need the equation for bright fringes. Here is what I got:

Using geometry I got the path difference between two rays to be (w / 2) * sinx [where x is the angle of the rays from the center horizontal]

Now I assume that for a bright fringe to occur, constructive interference must happen and so (w / 2) * sinx = m * P [where m is 1,2,3... and P is wavelength of laser] => sinx = (2m * P) / w

Also using geometry I was able to achieve that tanx = a / L

For small angles:

tanx = sinx so => a / L = (2mP) / w

=> P = (w * a) / (2L * M)

Now plugging in my values into that equation for the first fringe (m = 1) I get the wrong answer, my Laser's wave length is 645 nm, I got 316nm for an answer. (I am assuming a factor of 2 is the problem). Can anyone please help???

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# Single Slit Bright Fringes

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