1. Diffraction
Deriving
nl = d sin q

2. Diffraction
Diffraction results from the spreading out of waves passing through a gap.
The narrower the gap, the more the waves spread out.
If the gap is less than one wavelength, there is no diffraction at all.
Wavelength is not affected by diffraction.
Diffraction happens with all waves.
Single slit and multiple slit diffraction have nothing to do with Young’s double slits.
So don’t use the double slit formula.
Saturday, 01 December 2018
Leeds City College

3. Single Slit Diffraction
For a wide gap, there is not much diffraction.
Light rays
Sharp shadows
Single bright region
If the gap is made narrow, then we get to see a diffraction pattern
Light rays
Bright regions
Central bright region
Monochromatic light is needed for a clear pattern.
Saturday, 01 December 2018
Leeds City College

4. Intensity and diffraction
The observed pattern of bright and dark fringes can be explained by the superposition of secondary wavelets.
The intensity is greatest in the middle.
The bright fringes either side are much less intense.
The further we move away from the centre, the dimmer they are.
Saturday, 01 December 2018
Leeds City College

5. Equation Wavelength (m) Angle of spread.
Light rays
Bright regions
Central bright region
Wavelength (m)
Angle of spread.
If a is less than l, sin q > 1. That simply will not do.
Wavelength of light are in nano-metres (nm).
Convert to m.
1 nm = 1 × 10-9 m
Width of gap (m)
Saturday, 01 December 2018
Leeds City College

6. A further equation From the diagram we can see: D W Red light q
For very small angles, tan q = sin q
Since:
Rearranging:
we can write:
Saturday, 01 December 2018
Leeds City College

7. Linking with Double Slits
Fringe spacing
Width of the central bright fringe
Saturday, 01 December 2018
Leeds City College

8. Resolution Consider two objects very close together: Not resolved
Just resolved
Easily resolved
This was first worked out by John William Strutt, 3rd Lord Rayliegh.
It is often called Rayliegh’s criterion
Saturday, 01 December 2018
Leeds City College

9. Diffraction Grating There are two kinds of diffraction grating:
Transmission (where the light goes through);
Reflection (where the light is reflected).
The diffraction grating has the advantage over the double slit method of measuring wavelength in that:
the maxima are more sharply defined
the beam passes through more slits than two, so the intensity is brighter
the angles are larger so that they can be measured with greater precision.
Saturday, 01 December 2018
Leeds City College

10. How does diffraction work?q d
Monochromatic light, wavelength l
These rays go to the first bright fringe.
Monochromatic light is shone onto a transmission grating which has N lines per metre.
The slit spacing is given by:
Bright spots appear only when there is constructive interference, i.e. when light from A is in phase with B.
That happens when they are one whole wavelength apart.
Saturday, 01 December 2018
Leeds City College

11. Deriving the equation d q Let’s look in close up: AC = 1 l
Monochromatic light, wavelength l A B C q
AC = 1 l
AB = d
AC = d sin q
So we can write:
Therefore:
This is true for any of the bright spots, 1, 2, 3, …n
Saturday, 01 December 2018
Leeds City College

12. Be careful!
The diffraction grating is often given as lines per millimetre. You will have to convert to lines per metre.
750 lines per mm = 750 × 103 lines per metre.
d = 1.33 × 10-6 m.
In some gratings, the situation is even worse – they write N in lines per inch! (US–sourced gratings in particular.
10000 lines per inch = 393 per millimetre.
The maximum order of diffraction possible is limited by sin q < 1. If you find that n = 3.8, then the maximum orders possible is 3, NOT 4.
Wavelengths are in nanometres (nm)
1 nm = 1 × 10-9 m
Saturday, 01 December 2018
Leeds City College

13. Patterns of Diffraction
If the wavelength is reduced, we observe that the angle of each order is reduced.
If we have white light, we will see several coloured lines for each order.
Saturday, 01 December 2018
Leeds City College