Dispersion by diffraction grating

[Liketothink]

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.

 

[rickz02]

Are you sure of that that's the equation for diffraction? Checking the units, it's quite inconsistent... Check the equation again...

 

[Liketothink]

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.

 

[Liketothink]

Please help, I only have a couple of hours left.

 

[rickz02]

I got 56.502 cm, using the equation. we seem to get the same answer.