Young's double-slit experiment is a classic experiment that demonstrates the wave-like nature of light and the phenomenon of interference. In the experiment, light passes through two parallel slits and creates an interference pattern on a screen behind them.
When monochromatic light, which consists of a single wavelength, is used in the experiment, the interference pattern consists of alternating bright and dark fringes. This pattern occurs because the light waves from the two slits interfere with each other constructively at certain points (bright fringes) and destructively at other points (dark fringes). This interference arises from the superposition of the waves, where their amplitudes combine.
Now, let's consider the case of two different wavelengths of light being used simultaneously in the double-slit experiment. When two different wavelengths are present, each wavelength will create its own interference pattern independently. These patterns will overlap and produce a combined interference pattern on the screen.
The resulting interference pattern will exhibit a more complex structure compared to the case of a single wavelength. It will consist of a combination of the interference patterns generated by each wavelength individually. This phenomenon is known as "beat" or "moiré" patterns.
The beat pattern arises due to the variation in the phase difference between the waves of different wavelengths. At certain points, the waves will be in-phase and reinforce each other, leading to bright fringes, while at other points, they will be out-of-phase and cancel each other out, resulting in dark fringes.
The spacing and visibility of the resulting beat pattern depend on the specific wavelengths involved. If the two wavelengths are close together, the beat pattern will have a high frequency, resulting in closely spaced bright and dark fringes. On the other hand, if the wavelengths are significantly different, the beat pattern will have a lower frequency, with wider spacing between the fringes.
In summary, when two different wavelengths are used in Young's double-slit experiment, the resulting interference pattern is a combination of the individual interference patterns generated by each wavelength. This leads to a more complex interference pattern with alternating bright and dark fringes, known as a beat pattern.