Suppose two waves interfere constructively at some point, in a double slit experiment set-up. This essentially means that the two waves have their peaks and troughs in sync with each other, and there is a phase difference of $2n\pi$. However, it is said that, we obtain bright fringes where waves interfere constructively.
However, this seems to be somewhat of an approximation to me. At constructive interference, if a wave has a peak at some point on the screen, the other wave would also have a peak. Similarly, if one wave has a trough, then the other wave also has a trough. However, how can we be sure that the first wave would definitely have a peak or a trough at that point ? Why not any other point in between ?
As the wave is moving forward, we can think of the screen as some point $x_0$ along the direction in which the wave moves. As the wave moves forward, the point $x_0$ on the wave, can be the peak, trough or any other point depending on time. So, the amplitude at any point on the screen oscillates too.
Since the displacement of the field at the screen oscillate, shouldn't we get an oscillating or 'flickering' intensity fringe pattern, instead of a constant bright-dark pattern ? Shouldn't the bright regions flicker extremely fast ?
Will this be true, even in case of double slit diffraction ?
Best Answer
A detector, such as your eye, does not respond at the rate of oscillation of the optical or RF frequency, instead it responds to the variation of its peaks or to variation of its average power (energy per cycle). These variations are many orders of magnitude slower than the oscillation rate. For example your eyes can tell the difference of brightness but only at the rate of few hundred hertz. In an ideal double-slit experiment the nulls are completely zero non-oscillating in intensity, there really is no energy; at the intensity peaks those do fluctuate at the rate of the oscillation (optical or RF) frequency but the detector ignores that and responds to the peaks or rms energy.