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**Lesson 8 G3 Two Source Interference of Waves**

G4 The Diffraction Grating

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**Lesson 8 – 2 source interference**

State the conditions necessary to observe interference between two sources. Explain, by means of the principle of superposition, the interference pattern produced by waves from two coherent point sources (The effect may be illustrated using water waves and sound waves in addition to EM waves). Outline a double-slit experiment for light and draw the intensity distribution of the observed fringe pattern (This should be restricted to the situation where the slit width is small compared to the slit separation so that diffraction effects of a single slit on the pattern are not considered). Solve problems involving two-source interference.

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Superposition

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**Principle of superposition**

When two or more waves meet, the resultant displacement is the sum of the individual displacements

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**Constructive and destructive interference**

When two waves of the same frequency superimpose, we can get constructive interference or destructive interference. + = = +

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**Interference patterns**

Ripple Tank Simulation

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Path difference Whether there is constructive or destructive interference observed at a particular point depends on the path difference of the two waves

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**Constructive interference if path difference is a whole number of wavelengths**

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**Constructive interference if path difference is a whole number of wavelengths**

antinode

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**Destructive interference if path difference is a half number of wavelengths**

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**Destructive interference if path difference is a half number of wavelengths**

node

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**Two Source Superposition Experiments**

Demo: Superposition of Sound Waves microphone CRO Signal generator (3kHz) loudspeakers

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**Young’s double slit experiment**

Coloured filter

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**D P λ d O s P’ S1 T M S2 D = distance from slit to screen (few m)**

θ θ D = distance from slit to screen (few m) d = slit separation (0.5mm) s = distance from central maximum to first subsidiary maximum

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**sinθ = λ d tanθ = s D λ = s d D s = Dλ d**

At point P’, the path difference between waves from S1 and S2 is one whole wavelength. Thus they arrive in phase, constructively interfere and create a ‘bright fringe’. S1T = λ Distance D is large and the wavelength of the light is small so θ must also be very small. We can also approximate that angle S1TS2 is a right angle. Using the small angle approximation sinθ = tanθ = θ or... sinθ = λ d tanθ = s D λ = s d D s = Dλ d

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**The Diffraction Grating**

The diffraction grating is (in theory) a piece of opaque material with many parallel, equidistant and closely spaced transparent slits that transmit light. In practice lines are ruled onto glass with diamond leaving transparent glass in between.

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**Consider a grating with coherent, monochromatic light of wavelength λ incident upon it:**

B C A θ N Section of grating Light diffracted at θ to the normal Monochromatic light

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If light from any pair of slits reaching a point in the distance and causes maximum constructive interference, we know that the path difference must be a whole number of wavelengths... AN = nλ Hence... Thus light from all slits constructively interferes with that from every other at values of θ determined by the equation, producing bright regions. This gives rise to the different order spectra for any particular wavelength of light. d sinθ = nλ n = 0, 1, 2, 3 etc

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n = 2 n = 1 n = 0 Monochromatic light n = 1 Section of grating n = 2

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**Note d is the separation of slits on the grating**

Gratings are often labelled “200 lines/mm i.e. d = 0.001/200 m = 5 x 10-6 m

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Experiment Use a diffraction grating to determine the wavelength of laser light.

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**The Diffraction Grating**

The diffraction grating is (in theory) a piece of opaque material with many parallel, equidistant and closely spaced transparent slits that transmit light. In practice lines are ruled onto glass with diamond leaving transparent glass in between. Experiment: Observe a white light source through both coarse (100 lines/mm) and fine (500 lines/mm) gratings. Repeat placing red or green filters in front of the grating.

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**Observations for white light:**

The diffraction spectra of white light has a central white band (called the zero order image). On either side are bright bands of colour. The first red band is the ‘first order spectrum’ for that wavelength. Further out is another identical red band - the ‘second order spectrum’ etc. Bands for the visible spectrum are seen, with violet being nearest the centre and red furthest. A finer grating forms less orders, further apart than on a coarse grating.

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