Understanding interference in classical physics

Understanding interference in classical physics 

The theory of diffraction is the foundation for study of the double-slit interference experiment. When first performed in 1800 by Thomas Young (1773-1829), this experiment was considered definitive proof of the wave nature of light. We can modify the single-slit apparatus of Fig. 2.1 to suit Young's experiment by simply cutting a second slit in the diaphragm.

As shown in Fig. 2.3, the width of the second slit is the same as that of the first, w. We must position the second slit so that the two slits are close together-but not too close: for observable interference to occur, the slit separation s must be greater than w. Again, we shine a beam of monochromatic light of frequency v on the diaphragm and see what happens at the detector, which is far to the right of the diaphragm. Figure 2.3

This time, our detector shows an interference pattern like the one in Fig. 2.4. At first glance, this figure may look similar to the diffraction pattern of Fig. 2.2, but on closer examination we see striking differences. For one thing, the interference pattern exhibits more bright bands than the diffraction pattern. This means that the energy of the radiation scattered by the double-slit diaphragm is more evenly distributed than that scattered by a single slit. (In the diffraction pattern about 90% of the energy appears in the central band.) Finally, the individual bands in the interference pattern, which are called interference fringes, are narrower than those of the diffraction pattern.

If we study how the interference pattern changes as we fiddle with the incident wavelength ., the slit separation s, and the slit width w, we discover that the separation between the bright bands increases with increasing just as it did in the diffraction pattern, for which the separation is proportional to  /w. But also we find a difference: the separation in Fig. 2.4 is independent of the slit width w but is inversely proportional to the slit separation s.

The key to understanding interference is superposition. When the incident plane wave encounters the double-slit diaphragm it "splits," and a diffracted wave emerges from each slit. (In a sense, each slit becomes a source of radiation that travels to the detector.) These waves add in the region between the slit and the detector, and this device measures the intensity of their superposition . Now, at the detector the amplitudes of the electric fields of the diffracted waves are equal, but their phases are not. Consequently, their superposition manifests regions of constructive and destructive interference, as seen in Fig. 2.4.

The trick to deriving an equation for the intensity measured in the double-slit experiment-which we'll call is therefore to add the electric fields of the waves diffracted by each slit. (This step is legitimate because Maxwell's equation for these fields is linear.) Having done so, we could calculate the aforementioned phase difference and would find the field from the lower slit lags the field from the upper slit by an amount . The last step is to average the squared modulus of the total electric field at a point  on the detector over one period, which yields 

The source:

Michael A. Morrison - Understanding Quantum Physics.

By. Fady Tarek