# Basic diffraction grating question

1. Sep 15, 2010

### Grebulous

This is an intro lab-based question.

1. The problem statement, all variables and given/known data
I took a 650 nm red laser and shined it through a diffraction grating that claimed it had 13500 lines/inch, which comes to 5315 lines/cm in civilized people units. The grating was placed 30 cm away from a piece of paper on the wall. The distance between the central maximum (m=0) and the m=1 maximum was measured to be 4.1 cm. I'm trying to verify that the number of lines per cm is in fact around 5315.

2. Relevant equations
The grating equation, d sin(theta) = m(lambda)

3. The attempt at a solution
m=1 for the first maximum, and rearranging the equation, d = lambda/sin(theta). d equals the spacing between each slit, which is just 1/N, where N is the number of lines per cm. sin(theta) is 4.1/sqrt(30^2 + 4.1^2) = 0.1354. So, N = sin(theta)/lambda = 0.1354/(6.5 x 10^-5 cm) = 2080 lines/cm, to 3 s.f.

I find that answer odd - did I make some really basic mistake, or does the grating really have 2.5 times fewer lines than it claims it does? If I were to go the other way and assume N was right, I'd get an ultraviolet wavelength, and I double-checked my measurements. Can anybody spot my goof?

2. Sep 15, 2010