# Problem with Diffraction Grating Equation (results do not match theory)

1. Feb 13, 2012

### MnFeCo

Hi.

The grating equation says n x λ = d sinθ. Where d = 1/N (the nymber of slits per unit length.)

Using the equation and solving for a grating with large number of slits gives the result that the diffraction pattern should have a greater angle of deviation from central maximum for gratings with for example 600 slits per mm compared to 100 slits per mm.

I have a diffraction grating just like the above described. Using a green monochromatic led source I observe the patterns for the 600 slits per mm versus the 100 slits per mm.

I get completely opposite results to the theory. The 600 slits per mm grating gives a sharp well defined pattern but it is compressed into a small zone (not spread out).

Whereas the 100 slits per mm grating gives the very opposite. It has a wider diffraction pattern, much more spread out.

What is it that I am not seeing or doing wrong?

Because according to the n x Lambda = d sin theta we can arrange and get
:--> sinθ = n x λ / d
which for small d (large number of slits) gives a large theta angle.

But as I said, it does not do that in practice though it says so in theory.

Please guide/help me out on this.

Much appreciate any help offered.

Thank You

2. Feb 14, 2012

### technician

What you say is correct and I would doubt the information given about the gratings.how do you know that they do have 100 and 600 lines per mm?
Are you sure it is NOT 1000 lines per mm