Diffraction is the bending of waves around small obstacles and the spreading out of waves past small openings

Transcription

1 Diffraction

2 Diffraction is the bending of waves around small obstacles and the spreading out of waves past small openings

3 Diffraction by Pinhead

4 When λ the opening, max diffraction occurs When λ < opening size, little diffraction occurs

5 Long waves diffract more than short waves After diffraction, a wave will have the same speed, frequency and wavelength

6 Young s experiment In 1801 Thomas Young showed wave nature of light by passing monochromatic light through two narrow slits He discovered that a series of bright and dark bands appeared on a screen behind the slits and the bright bands were the same distance apart

7 The waves passing through the second barrier were in phase so they could interfere with each other when they arrived at the screen He concluded that light traveled as a wave and that the pattern was due to interference of the diffracted waves The bright bands are antinodes (maxima) and the dark bands are nodes (minima)

8 In Phase Waves

9 180 o Out of Phase Waves

10 Waves of different λ

11 Two slit diffraction & interference of green laser light

12 Central bright spot

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14 The central maximum is formed by waves passing through S 1 and S 2 diffracting the same amount and arriving at the screen in phase (constructive interference) waves meet in phase at screen (trough meets trough)

15 The dark areas (minima) are formed by destructive interference waves meet out of phase at screen (crest meets trough) light going through one slit travels a greater distance and is ½ λ out of phase at the screen the extra distance is an odd number of ½ λ

16 the other bright areas are formed by light reaching the screen in phase (the extra distance is some whole-number multiple of a wavelength)

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18 Young derived an equation to calculate the wavelength of light x = distance from centre bright band to some other bright band (maximum) d = distance between the slits L = distance from slits to screen n = order of the bright band (1, 2, 3, etc.) λ = xd nl equation is valid IF the angle of diffraction is small (< 10 degrees)

19 For θ < 10 o sin θ tan θ tanθ = x L

20 Example A screen is 1.2 m from two narrow slits. The slits are a distance of 3.0 x 10-5 m apart. The second order maximum is 4.5 x 10-2 m from the central maximum. Determine the wavelength of light.

21 Solution λ λ = = xd nl m m ( m) 21.2

22 If the angle of diffraction is measured, or if θ > 10 o or if x L, λ = d sinθ the equation becomes n

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24 Example Monochromatic light falls on 2 slits mm apart producing a 4 th order maximum at a 6.40 o angle. What is the wavelength of light?

25 Solution λ = d sinθ n λ = m 4 o sin 6.40 λ = m

26 Example Monochromatic light passes through 2 slits 3.0 x 10-5 m apart. The 2 nd order maximum forms on a screen 1.1 m away and is 0.37 m from the central maximum. Determine λ.

27 Solution λ = λ = xd nl m ( m) ( m) 21.1 λ =5.0 x 10-6 m

28 Solution θ = o λ = d sinθ n λ = 5 3.0x10 m sin o 2 λ = m

29 Double slit

30 4 slits

31 5 slits

32 Diffraction Gratings if the 2 slits in Young s experiment are replaced by a series of narrow slits, an interference pattern is still formed the pattern of bright and dark bands is much sharper and narrower than with 2 slits the equations remain the same

33 diffraction gratings are usually marked with the number of slits per cm or per mm (called the line density) d = 1 lines per metre

34 Example A diffraction grating has 550 lines per mm. A first order maximum is produced m from the central bright band when the screen is m from the grating. Determine the wavelength of light.

35 Solution d 550 lines/mm = lines/m 1 x θ = tan = L = 1 = m lines per metre o λ = λ = d sin θ n m sin o λ = 6.50 x 10-7 m

36 Red & blue light through a grating

37 Poisson s Bright Spot Fresnel developed a comprehensive mathematical wave model for light. Simon Poisson used Fresnel's equations to demonstrate that they made an absurd prediction: If a narrow beam of light were shone upon a small object, waves would diffract around the object and constructively interfere in the middle of the shadow, making a bright spot there.

38 According to particle theory, constructive interference at the centre was impossible When the experiment was done, the spot was visible

39 Beta Andromedae: ~ 200 light-years, a red giant star, cooler than the Sun but much larger Diffraction Spikes

40 The secondary mirror in a reflecting telescope has to be positioned at the central axis of the telescope and so has to be held by struts within the telescopes tube. No matter how fine these support rods are they diffract the incoming light from a subject star