10.3.1 Double Slit Interference Pattern

If two sound waves in anti-phase superpose destructively to result in silence, then two light waves in anti-phase should also superpose destructively to result in darkness.

In the past, it was quite challenging to set up light sources and narrow slits suitable to demonstrate the interference of light. Today, we can buy laser pointers and double-slits from the internet. Look and behold, when we shine a laser beam through two very narrow slits (called a double-slit), we obtain a beautiful pattern of regularly spaced bright and dark spots on a screen.

So what’s producing those bright and dot spots? The slits, being lit up by the laser beam, act like two in-phase light sources, emitting two coherent light waves propagating towards the screen. The two light waves travel different distances to arrive at each position on the screen. At locations where the two light waves arrive in-phase, bright spots are formed. At locations where they arrive in antiphase, dark spots are formed.

Basically, the double-slit interference pattern is the ripple tank interference pattern performed with light instead of water waves, with a few key differences:

The air is basically transparent to light. For this reason, we can only see the fringes on the screen. We don’t see the nodal and anti-nodal lines in the space between the slits and the screen.
Visible light is an EM wave with frequency of ~10¹⁴ Hz. The human eye cannot track the oscillation of the electric field strength. While we can see the water level rising and falling in the ripple tank, we cannot “see” the time-varying “displacement” of the light wave on the screen. All we can “see” is the amplitude and intensity of the light wave.
The distance between the slits is extremely short compared to the distance to the screen (so the diagram above is not reflective of the true scale). This resulting geometry actually makes the calculations for the double-slit a lot easier (with the $\delta =d\sin \theta$ formula) and the fringe separations constant (with the $\displaystyle \Delta y=\frac{{L\lambda }}{d}$ formula). These two points will be elaborated in the next two sections.