# Diffraction grating (missing diffraction beam)

1. May 9, 2010

### pfellas

1. The problem statement, all variables and given/known data
A diffraction grating has slit width 0.83 micrometres. When light of 430 nanometres is used, diffracted beams are observed at 14 degrees 55 minutes and at 50 degrees 40 minutes to the zero order. The first beam is assumed to be the first order and the other one can be calculated to be the third order. Why is the second order missing?

2. Relevant equations
d Sin (theta) = n x Lamda

3. The attempt at a solution
I know that the slit width has something to do with this. Does the width of the slit cause a single slit effect which counteracts the diffraction effects for the 2nd order only but allows the first and third order to be visible?

Last edited: May 9, 2010
2. May 9, 2010

### Redbelly98

Staff Emeritus
Welcome to Physics Forums
That could well be what is going on. [EDIT: see my post #5 below] [STRIKE]But to me it seems to be a weird setup, to have such a narrow slit combined with a diffraction grating. I have a hard time imagining how they are combined, is there any other information in the problem statement? Do they say or indicate if this is a transmission or reflection grating?[/STRIKE]

At any rate, you can use the given information to calculate:
• The grating spacing
• The angle of the 2nd-order diffracted beam
• The angle of the single-slit dark band
Then you can compare those two angles, and see if they are equal.

Last edited: May 11, 2010
3. May 10, 2010

### rl.bhat

In a diffraction grating, you can see the interference pattern due to double slit and diffraction pattern due to single slit. If a is the slit width, b is the spacing, then (a+b) will be the distance between the slits. If θ is the angle of diffraction of nth maximum due to interference, then we have
(a+b)sinθ = nλ.
If α is the angle of diffraction for pth minimum due to diffraction, then
a*sinα = πλ.
If you keep a constant and change b, the spacing between the interference maxima changes.
At a certain value of a and b, it is possible that , for the same value of θ, certain interference maximum may coincide with diffraction minima at the same position on the screen. when this happen, those maxima will not be visible and they are called the missing orders.
When a = b, second, fourth, sixth etc., orders of interference maxima are missing.
When 2a = b, third, sixth, ninth..etc., orders are missing.

4. May 11, 2010

### pfellas

Thank you both very much! Much appreciated.

5. May 11, 2010

### Redbelly98

Staff Emeritus
You're welcome.

After reading rl.bhat's response, I realize now that the grating is made of many slits, each of the given 0.83 μm width, and to-be-determined spacing. So it's a transmission grating, not a reflection grating as I am used to seeing in practice.