- #1

perplexabot

Gold Member

- 329

- 5

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???