Diffraction

1. Diffraction Deriving nl = d sinq

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. Leeds City College

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

4. Intensity 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. Leeds City College

5. Bright regions Central bright region Light rays Equation Wavelength (m) Angle of spread. If a is less than l, sinq > 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) 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: Leeds City College

7. Linking with Double Slits Fringe spacing Width of the central bright fringe 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 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. Leeds City College

10. How does diffraction work? Monochromatic light, wavelength l These rays go to the first bright fringe. d q 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. Leeds City College

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