Diffraction Question: Calculating m

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SUMMARY

The discussion focuses on calculating the minimum width of a screen required to capture all principal maxima from a diffraction grating with 5620 lines per centimeter and a light wavelength of 471 nm. The equation used is sin(theta) = m * wavelength / width, where m represents the order of the maxima. The solution indicates that for m = +1 and m = -1, the calculated width of the screen must be 1.95 m to accommodate the spread of the diffraction pattern.

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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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