1. 11.3 – Single slit diffraction

2. Comparing double and single slit diffraction

3. Deriving the equation for the 1st minimum of the single slit diffraction pattern
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Coherent light waves
Position of 1st minimum θ

4. Deriving the equation θ = λ/b

5. We assume that the interference pattern is produced by light from the bottom half of the slit interfering with light from the top half of the slit
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Position of 1st minimum B P A

6. θ For destructive interference path difference = ½ λ ½ λ = BP - AP
Position of 1st minimum P A θ θ
½ slit width b
Path difference B

7. Deriving the equation sin θ = λ / b
Use the diagram and simple trigonometry to derive the equation for the angle of the 1st minimum (θ) for a single slit interference pattern.
Can you show that for very small angles sin (θ) in degrees is approximately equal to θ in radians
(hint – produce a table showing values of sin (θ) using degrees and θ in radians, what do you notice?)
Use the equation you have derived, the laser and single slit to estimate the wavelength of the red laser light.

8. Resolution
When light from two sources passes through a narrow aperture an interference pattern in produced
If the angular separation of the light from the two sources is too small the interference patterns will overlap in a way that prevents you from distinguishing (resolving) the two sources

9. Resolution
Astronomers use to think that all the bright lights in the night sky were individual stars. We now know that many of those bright lights are actually galaxies, i.e. billions of stars grouped together.
How close to us do two light sources have to be for us to tell them apart (resolve them)?

10. Two resolved light sources

11. Two unresolved light sources

12. THE RAYLEIGH CRITERION
Rayleigh suggested by how much they should be separated in order for the two sources to be just resolved.
the two sources will just be resolved  If the central maximum of one diffraction pattern coincides with the first minima of the other diffraction pattern then
This is known as the Rayleigh Criterion.

13. Where  is measured in radians
Rayleigh criteria for circular aperture
Two sources of light are just resolved when:
the 1st minimum of one diffraction pattern is located on top of the central maximum of the other diffraction pattern
Where  is measured in radians