Dispersion by diffraction grating

AI Thread Summary
The discussion revolves around calculating the width of the first-order spectrum produced by a diffraction grating when white light passes through it. The relevant equation used is y = m * L * wavelength / d, where d is the grating spacing derived from the number of lines per cm. The user initially calculated the spectrum width as 56.486 cm, but faced inconsistencies in their results. After some back-and-forth, they confirmed that using the equation correctly yields a similar answer of 56.502 cm. The conversation emphasizes the importance of unit consistency and verifying the application of the diffraction equation.
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Homework Statement



White light containing wavelengths from 396 nm to 756 nm falls on a grating with 7300 lines/cm. How wide is the first-order spectrum on a screen 2.15 m away?

Homework Equations


y=m*L*wavelenth/(d)


The Attempt at a Solution


using the equation I have found y1 to be 62.149 and y2 118.635. I took the difference of the two which gave me 56.486 cm, but that is wrong for some reason. Please help.
 
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Are you sure of that that's the equation for diffraction? Checking the units, it's quite inconsistent... Check the equation again...
 
That's the equation I'm used to. If we assume that the angle is small then sintheta=y/L
dsintheta=m*wavelength
d(y/L)=m*wavelength
m*wavelength*L/(d)=y ? I don't know what's wrong with the equation. For the units I converted everything to cm because 1/7300=d in cm.
 
Please help, I only have a couple of hours left.
 
I got 56.502 cm, using the equation. we seem to get the same answer.
 
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