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Let us now consider the classical interference of light waves. Figure 5
shows a standard doubleslit interference experiment in which monochromatic plane light waves are normally incident on two narrow parallel
slits which are a distance apart. The light from the two slits is projected onto
a screen a distance behind them, where .
Figure 5:
Classical doubleslit interference of light.

Consider some point
on the screen which is located a distance from the centreline, as shown in the figure.
Light from the first slit travels a distance to get to this point, whereas
light from the second slit travels a slightly different distance . It is
easily demonstrated that

(63) 
provided .
It follows from Eq. (46), and the wellknown fact that light waves are superposible, that the wavefunction at the point in
question can be written

(64) 
where and are the wavefunctions at the first and
second slits, respectively.
However,

(65) 
since the two slits are assumed to be
illuminated by inphase light waves of equal amplitude. (Note that we are ignoring the difference in amplitude
of the waves from the two slits at the screen, due to the slight difference between and , compared to the difference in their phases.
This is reasonable provided .) Now, the intensity (i.e., the energy flux) of the
light at some point on the projection screen is approximately equal to the energy density of the light at this point times the velocity of light (provided that ). Hence, it follows from Eq. (56)
that the light intensity on the screen a distance from the centerline is

(66) 
Using Eqs. (63)(66), we obtain

(67) 
Figure 6 shows the characteristic interference pattern corresponding to the above expression. This pattern consists of equally spaced light and dark bands
of characteristic width

(68) 
Figure 6:
Classical doubleslit interference pattern.

Next: Quantum Interference of Light
Up: WaveParticle Duality
Previous: Quantum Theory of Light
Richard Fitzpatrick
20100720