The question is: A 544 line/mm diffraction grating isilluminated by light of wav

Question

The question is: A 544 line/mm diffraction grating isilluminated by light of wavelength 487 nm. How many bright fringesare seen on a 1.68-m-wide screen located 1.1 m behind thegrating? The question is asking for m. But, howdo I find ym? When I use 1.68m as my ym I am getting the wronganswer for m. I am confident everything else that I am doing isright, it's just the ym that I am not sure on. The question is asking for m. But, howdo I find ym? When I use 1.68m as my ym I am getting the wronganswer for m. I am confident everything else that I am doing isright, it's just the ym that I am not sure on.

Explanation / Answer

I'll give it a shot: dsin = m grating is 544line/mm multiply top and bottom by 1000 toconvert to m then take the reciprocal of that: 1/544000 = 1.838 *10-6 Next find : Creating a right triangle with the screen it's 1.68-m-wide sodivide by 2 and get .84m a2 + b2 = c2 1.12 + .842 = c2 (1.12 + .842) = c c = 1.30685m Back to dsin = m (1.12 + .842) = c c = 1.30685m Back to dsin = m (1.838 * 10-6)sin(.84m/1.30685m) = m(4.87 *10-9) m = 4.23 but since that's only half of the screenmultiply by 2 and get 8.468 Been awhile since I've done this kind of problem, but I gaveit a shot, good luck, hope that helps. Been awhile since I've done this kind of problem, but I gaveit a shot, good luck, hope that helps.

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