1. Waves: Diffraction Gratings
Learning Objectives
Book Reference : Pages
To understand diffraction gratings
To understand how changing wavelength and slit size affect the transmitted pattern
To understand how the diffraction grating equation is derived
To be able to complete diffraction grating related calculations

2. Diffraction Gratings : Definition
A diffraction grating is plate with many parallel slits in it.

3. Diffraction Gratings : Key Results
Light passing through each slit is diffracted
The Diffracted light wave from adjacent slits interfere, (reinforce each other) in certain directions only

4. Diffraction Gratings : Terminology
The central beam is referred to as the “zero order beam”
The other beams are numbered outwards on each side: 1st order, 2nd order etc

5. Diffraction Gratings : Experimental Questions
How does the diffraction pattern change with wavelength?
How does the diffraction pattern change with slit distance?
Virtual Physics Lab : Waves  Diffraction

6. Diffraction Gratings : Experimental Findings
How does the diffraction pattern change with wavelength?
How does the diffraction pattern change with slit distance?
The angle of diffraction between each beam and the zero order beam increases with increasing wavelength (Blue to Red)
The angle of diffraction between each beam and the zero order beam increases with decreasing gap size

7. Diffraction Gratings : Analysis 1
Each diffracted wavefront reinforces an adjacent wavefront
Wavefront at P reinforces wavefront at Y one cycle earlier which in turn reinforces wavefront at R one cycle earlier
This forms a new wavefront PYZ which travels in a certain direction and forms a diffracted beam

8. Diffraction Gratings : Analysis 2
Formation of nth order beam
Wavefront at P reinforces wavefront from Q emitted n cycles earlier.
Wavefront from Q has travelled n wavelengths.
QY is n
sin  = QY/QP (substitute)
sin  = n /d (rearrange)
dsin  = n  P Q Y d
Where d is the slit separation, n is the order of the diffracted beam and  is the wavelength

9. Diffraction Gratings : Analysis 3
Notes
The number of slits per metre N is 1/d
As d decreases the angle of diffraction increases. (As N increases, the angle of diffraction increases)
Maximum number of orders is when  = 90° and hence sin  = 1
n = d/
(Rounded down to the nearest whole number)

10. Problems 1
A laser of wavelength 630nm is directed normally at a diffraction grating with 300 lines per mm. Calculate :
The angle of diffraction for the first two orders [10.9° & 22.2°]
The number of diffracted orders produced [5]

11. Problems 2
Light incident normally on a diffraction grating with 600 lines per mm contains wavelengths of 580nm and 586nm only.
How many diffracted orders are seen in the transmitted light [2]
For the highest order calculate the angle between the two diffracted beams [0.58°]

12. Problems 3
Light of wavelength 480nm is incident normally on a diffraction grating the 1st order transmitted beams are at 28° to the zero order beam. Calculate:
The number of slits per mm for the grating [1092]
The angle of diffraction for each of the other diffracted orders [69.9°]