# 10.3.4 Young’s Double Slit Experimental Set-up

Historically, the double-slit interference pattern provided the first evidence of interference of light, which proved beyond doubt that light is indeed a wave[1]. But what took us so long to notice the interference of light?

Coherence

It turns out that light waves are quite “erratic”. An ordinary light source consists of a very large number of randomly oriented atomic emitters. Each excited atom radiates a polarized wavetrain for roughly 10-8 s. All these wavetrains superpose to form a resultant wave whose phase (and polarization) changes continuously in a completely unpredictable fashion[2]. This means that with two independent light sources such as two light bulbs, we get two incoherent light waves. In such a situation, the resultant intensity at every point on the screen (averaged over time) is simply the summation of the two intensities. This is why when we switch on two light bulbs, we get double the brightness everywhere, not bright fringes here and dark fringes there!

So how did Thomas Young obtain two coherent light sources? Well, instead of looking for a magic light beam that maintains the phase within itself and over time (which the laser is), he simply shone both the slits with one single light source. The light waves leaving the two slits will still be changing phase randomly with time. But since they originated from the same light source, their phases are changing randomly but in the exact same way as each other. This means that the light waves leaving the two slits are actually coherent with each other. Genius.

Point Source

Traditionally, an additional narrow slit is inserted before the double-slit. The purpose of the single slit is simply to reduce the width of the light source[3]. In other words, we are trying to obtain a line or point source, instead of an extended source. This is necessary because every point in an extended light source acts as an independent light source, each producing its own interference pattern which is slightly misaligned with those produced by neighbouring points in the extended light source. When these interference patterns overlap, the dark fringes will get filled up. The interference pattern will be “smudged” and become unrecognisable.

Example

The main features of the apparatus for a double-slit interference demonstration, and some of the typical dimensions are illustrated in the diagram below.

Calculate the separation of the bright fringes on the screen if

a) light of wavelength 600 nm is used.

b) light of wavelength 400 nm is used.

Solution

a)

\displaystyle \begin{aligned}(\Delta y&=\frac{{L\lambda }}{d})\\\Delta y&=\frac{{1.50(600\times {{{10}}^{{-9}}})}}{{3.0\times {{{10}}^{{-3}}}}}\\&=0.30\text{ mm}\end{aligned}

(Note that d is the centre-of-slit to centre-of-slit distance)

b)

Since $\Delta y\propto \lambda$,

$\displaystyle \Delta {{y}_{{400}}}=\frac{{400}}{{600}}\Delta {{y}_{{600}}}=\frac{2}{3}\times 0.30=0.20\text{ mm}$

(Note that fringe separation is proportional to wavelength. So red light form wider fringes than blue light)

Animation

Olympus

[1] Until the photoelectric effect proved beyond doubt that light is a stream of particles called photons. Well, this is how science works: we modify our understanding as we take in new evidences. You will learn about the photoelectric effect in the topic of quantum physics.

[2] Mathematically, natural light is modelled as two arbitrary, incoherent, perpendicularly polarized waves of equal amplitude.

[3] It is not to diffract (i.e. spread) the light per se, as taught in many schools.