1. DIFFRACTION DIFFRACTION
John Parkinson

2. Single Slit Diffraction
THE BENDING OF WAVES AROUND CORNERS
- PAST AN OBSTACLE OR THROUGH A GAP
Barrier
Ripple Tank Image
Single Slit Diffraction
Wave Height
- Intensity
John Parkinson

3. Subsequent position of wavefront
WAVEFRONT FORMATION
Subsequent position of wavefront
“Every point on a wavefront acts as a source of secondary waves which travel with the speed of the wave.
At some subsequent time the envelope of the secondary waves represents the new position of the wavefront.”
Secondary sources
Original wavefront
John Parkinson

4. The diffraction grating
A prism splits white light up into its various wavelengths
A diffraction grating gives a similar result so it is useful when analysing
various wavelengths being emitted.
Structure:
Glass etched
with a diamond cutter
with 300 lines per mm
Each ‘gap’ is only a few wavelengths wide so diffraction occurs at each one
John Parkinson

5. n = 1 λ corresponds to a path difference of one wavelength
The diffraction grating
Each slit effectively acts as a source of secondary waves, which add according to the principle of superposition
n= 0 λ
n = 1λ
n = 2λ
n = 1 λ corresponds to a path difference of one wavelength
John Parkinson

6. n = 1 when the path difference = 1λ
For light from slits A &B to add constructively, the path difference (AC), equals a whole number of wavelengths. (nλ)
Grating
Monochromatic light A C
Grating element d  B
n = 1 when the path difference = 1λ
sin θ = AC / AB
AB sin  = AC
Hence: d sin  = n
John Parkinson

7. DIFFRACTION GRATINGS WITH WHITE LIGHT
PRODUCE SPECTRA
400nm
500nm
600nm
700nm UV IR
John Parkinson

8. A spectrum will result DIFFRACTION GRATING WITH WHITE LIGHT
Hence in any order red light will be more diffracted than blue.
A spectrum will result
Several spectra will be seen, the number depending upon the value of d
screen
Second Order maximum, n = 2
Grating
First Order maximum, n = 1
White Central maximum, n = 0
First Order maximum, n = 1
Second Order maximum, n = 2
John Parkinson

9. Note that higher orders, as with 2 and 3 here, can overlap
Be aware that in the spectrum produced by a prism, it is the blue light which is most deviated
grating
John Parkinson

10. Hence there are 7 orders in all (white central order + 3 on each side)
QUESTION 1
Given a grating with 400 lines/mm, how many orders of the entire visible spectrum (400 – 700 nm) can be produced?
Finding the spacing d of the “slits” (lines).
d = 1/400 = 2.5 x 10-3 mm = 2.5 x 10-6 m
n = d sin 
n = d sin  / 
[sin  = a maximum of 1 at 900]
Why do we use 700 nm?
Hence there are 7 orders in all (white central order + 3 on each side)
John Parkinson

11. For red light in the second order For blue light in the second order
Question 2: Visible light includes wavelengths from approximately 400 nm (blue) to 700 nm (red). Find the angular width of the second order spectrum produced by a grating ruled with 400 lines/mm.
nλ = d sin θ
As before d = 2.5 x m
nλ = sin θ d
For red light in the second order
For blue light in the second order
= 15.40
John Parkinson