Diffraction Question: Calculating m

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To determine the minimum width of the observation screen for a diffraction grating with 5620 lines per centimeter and a light wavelength of 471 nm, the equation sin(theta) = m*wavelength/width is used. The user identifies that the principal maxima occur at m = +1 and m = -1, leading to a calculated angle of 0.265m. The solution requires calculating the spread of the maxima based on this angle and the distance from the grating to the screen, which is 0.750 m. The final answer, as provided in the reference material, is 1.95 m for the screen width.
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Diffraction Question: Calculating m...

Homework Statement



There are 5620 lines per centimeter in a grating that is used with light whose wavelength is 471 nm. A flat observation screen is located at a distance of 0.750 m from the grating. What is the minimum width that the screen must have so the centers of all the principal maxima formed on either side of the central maximum fall on the screen?

Homework Equations



sin(theta) = m*wavelength/width

The Attempt at a Solution



I realized that we were missing m from the problem...so I setup the equation sin (theta) = m*wavelength/w = m (471 x 10^-9 m/ .01/5620) = 0.265m

I can't proceed from there...It's quite confusing. can someone help me complete this problem? Thanks!

By the way, the book answer is 1.95 m
 
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The principal maxima are given when m = +1 and m=-1. Calculate the angle between them, then use the distance between the screen and grating to get the spread. Draw a diagram.
 

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