I can't figure out what I am doing wrong Getting Frustrated

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SUMMARY

The discussion revolves around calculating the slit spacing of a diffraction grating illuminated by a helium-neon laser with a wavelength of 629 nm. The user initially miscalculated the angle using an incorrect tangent function, resulting in an erroneous value for the slit spacing. The correct approach involves recognizing that the distance between the m=3 bright fringes is 33 cm, which corresponds to an angle of 5.43º for each fringe. Using the equation d = m*λ/sin(θ) with the correct angle yields the accurate slit spacing.

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I can't figure out what I am doing wrong! Getting Frustrated!

Homework Statement


A helium-neon laser (λ=629 nm) illuminates a diffraction grating. The distance between the two m=3 bright fringes is 33 cm on a screen 1.72 m behind the grating. What is the spacing between slits of the grating?


Homework Equations


Lamda = 629 nm
m = 3
y = 0.33 m
L = 1.72 m
d = ?


The Attempt at a Solution


What I did was tan theta = y/L = 0.33/1.72 = 1086 degrees
then I used the equation d*sin theta = m*lamda
and solved for d... d = m*lamda/sin theta = 1.00x10^-5 m but I am getting it wrong...what am I not doing right?
 
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If I'm understanding this problem statement correctly, it is giving you the distance between the m=3 maxima on either side of the midline. This means that each of these fringes is half of 10.86º away from the midline, or 5.43º.

So I think this may be the angle you are to use in the diffraction equation, with m = 3 and lambda = 629·10^-9 m.
 
oh ok thank you that's it!
 

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