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Light interference

Light acts as a wave, so different portions of a light beam appear brighter or dimmer due to the interaction of the electromagnetic field in the waves. Intensity is proportional to the square of the electric field. If E = E0 sin
wt, then I = E02/8p. If E from one wavelet interacts with another wavelet, the phase shift between the two waves modifies the observable intensity, I = E02 |cos f|/8p, where f is the phase shift. When f = p/2 or 3p/2 radians, the intensity goes to 0. This is illustrated in the figure below. The upper wave is taken as the reference phase. In the left-hand inset, the second wave is in phase, giving an output with the same phase and summed amplitude. In the middle inset, the second wave lags the first by 1/4 wavelength (p/2 radians, giving f = p/4), so the sum is reduced in amplitude compared to the first case. In the last inset, the two waves are shifted by half a wavelength (p radians, giving f = p/2), and the summed electric field vanishes (see the flat line?).

Click on a thumbnail image below to see a bigger image for the shifts:
Spectrometers -- Diffraction Gratings 1
Interference_In_Phase

Interference_In_Phase

Interference_Quarterwave_Shift

Interference_Quarterwave_Shift

Interference_Halfwave_Shift

Interference_Halfwave_Shift

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