# Why does interference pattern remain constant?

In the double slit experiment we have something like this

Light waves from two sources interfere at screen to give us this pattern. To reach the middle (that is a point on the perpendicular bisector) of measurement screen waves will travel equal distances (at sources they are in phase because of the same main source) and hence will be in phase at the middle of the screen and hence a constructive interference will occur.

We can write things a little more mathematically, if at time $$t$$ the crest of the light wave is at the sources (secondary) then at time $$t+nT$$ ($$T$$ is the time period) crests will be at the middle of the measurement screen and hence a maximum will occur. Here, I have assumed, for simplicity, that distance between the source $$S_1$$ and the middle point M is $$n\lambda$$.

Now, my question is when there was a crest at $$S_1$$ and $$S_2$$ then we had a maximum at $$M$$, but when there is no disturbance at sources (I mean $$E(t)=0$$ and $$B(t)=0$$) then there should be no disturbance at M too and therefore we should obtain a dark fringe (no light) for this particular interference. Why does the interference pattern remains static? The bright fringes should be turning on and off periodically.

My question comes down to normal light also, why do we see the light even when the electric field and magnetic field components reach their zero position periodically? We should see light as being turning on and off, off when $$E(t)$$ and $$B(t)$$ becomes zero and on for every other time.

P.S. :- My $$M$$ in the figure doesn't coincide with the maximum but by $$M$$ I meant the middle of the screen where the first maximum gonna occur.

• You are quite correct, but the frequency of visible light is of order $10^{15}$ Hz, so the oscillations in brightness at M are too rapid to see. – John Rennie Dec 28 '19 at 20:17
• Keep in mind that every time you see a visible light the field strength is oscillating. Any detector system which registered the temporal oscillations of an interference fringe would also register the temporal oscillations of a plain light source. – dmckee --- ex-moderator kitten Dec 29 '19 at 0:38

## 1 Answer

The interference of waves at M does in fact result in an oscillation which has the same frequency as the waves from S. You do not see this oscillation using light because it is around $$10^{14}-10^{15}$$ cycles per second, which is many orders of magnitude faster than what your brain can detect. If you did the experiment using water waves at no more than a few cycles per second you would see the oscillation.

The interference pattern is a sinusoidal variation in the amplitude (or intensity) of the oscillations of the light or sound waves. This pattern is a variation in space (from one point to another) but it is constant in time - because the amplitudes and phase differences of waves from the two slits remain constant in time. There is still a wave oscillation at each point on the screen, but there is also a sinusoidal variation in the amplitude of these waves across the screen.

You can see the oscillation in this video simulation of water wave, as the waves hit the wall/screen at 0.09 onwards. (It is a short video so I recommend re-setting the playback speed to 0.25.) Where there is constructive interference (bright interference fringe) large-amplitude waves are reaching the screen. Where there is destructive interference (dark interference fringe) the waves reaching the screen have small or zero amplitude.

• As in these simulations: phet.colorado.edu/en/simulation/wave-interference – Pieter Dec 28 '19 at 20:32
• I wouldn’t say the interference oscillates: in a bright fringe it remains constructive at all times. But the net amplitude oscillates. – dmckee --- ex-moderator kitten Dec 28 '19 at 20:47
• @dmckee Thanks for the suggestion. Yes there is a spatial oscillation (variation) in the amplitude, but I am trying to point out that there is still a time-oscillation of waves resulting from interference. – sammy gerbil Dec 28 '19 at 20:51
• Perhaps I wasn't clear. At any given point in space: (a) net amplitude oscillates in time and (b) but the phase difference (and thus the nature of the interference (fully constructive, fully destructive, partial)) remains constant in time. – dmckee --- ex-moderator kitten Dec 29 '19 at 0:37