A: Wave Phenomena

1. A: Wave Phenomena A.4 Single Slit Diffraction

2. What’s Diffraction again? • Diffraction is the bending of waves around a corner or through an opening (hole). The larger the aperture size (slit width) compared to the wavelength of the wave, the less the wave diffracts. Condition for noticeable diffraction: Size of opening should be approximately equal to the wavelength (opening ≈ λ of waves)

3. Single Slit Diffraction We have already established that diffraction will occur at an aperture of width b if λ ≥ b When light is shone at a very thin gap (a ‘slit’), it also diffracts. A diffraction pattern is produced on a screen placed a large distance from the slit:

4. Central maximum First minimum First subsidiary maximum

5. Explaining The Single Slit Diffraction Pattern This can be explained if we imagine that all points along the slit width behave as sources emitting secondary wavefronts. (This is called Huygens principle). If two of these secondary waves meet at a point distant from the slit, they will superimpose upon each other. Crest + crest = Constructive Int. = Bright spot Trough + crest = Destructive Int. = Darker spot

6. p = point far from the slit. p θ b If these two waves are to superimpose upon each other at p then they must meet. However, we assume that the point is so far away that the two waves are approximately parallel.

7. First minimum Darkness is formed. The two waves cancel out. So the bottom one travels ½ λ further than the top one. sin θ = ½ λ= λ ½ b b If θ is very small then sin θ ≈ θ so... To first minimum θ b θ ½ λ θ = λ b

9. Extra note: We know that for appreciable diffraction to take place, λ ≥ b. If λ = b then sinθ=1 so θ would be 90 degrees. i.e. There are no subsidiary maxima. This highlights that diffraction is the spreading out of the wave and does not necessarily show interference maxima and minima.

10. Simulations Effect of λ on θ: Java applet 1 Java applet 3

11. Experiment 1. Use the laser and single slit to produce a diffraction pattern. 2. Take measurements (including the ‘half width’ d) and thus determine the slit width b. (λred = 700 nm) d θ First minimum b Central maximum

12. Diffraction from a circular aperture The angle of the position of the first minimum in this situation is given by the formula... θ = 1.22 λ b

13. Teaser In the next Option G, we will look at Double-Slit Diffraction.