33: Interference
- Page ID
- 166349
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In 1801 Thomas Young set out to settle an argument that had run for more than a century. Newton had insisted that light was a stream of tiny particles (corpuscles) that flew in straight lines. A few dissenters, Huygens among them, held that light was a wave. The question seemed almost impossible to decide: light shows none of the obvious wave behavior of water or sound. Then Young sent light through two narrow, closely spaced slits and let it fall on a screen. If light were a hail of particles, he should have seen two bright bands, one behind each slit: the pattern that paint-covered balls thrown at a wall would make. Instead he saw a whole row of bright and dark stripes, many more than two, fading off to either side.
There is only one way to make stripes like that: the light from the two slits must be adding in some places and canceling in others, exactly as two sets of ripples do where they cross on a pond. Light is a wave. This chapter is about what follows from that single fact: how overlapping light waves reinforce and cancel, a phenomenon called interference, and how we read the resulting patterns to measure wavelengths, film thicknesses, and distances to a fraction of a wavelength. We will end with the instrument, the interferometer, that turns interference into the most precise measuring tool ever built: precise enough, two centuries after Young, to detect a passing gravitational wave that changes a \(4\,\mathrm{km}\) arm by a small fraction of the width of a proton. And we will circle back to the deepest puzzle of all: the same experiment, run with electrons, makes the same stripes.
Learning Objectives
- Explain the conditions for coherent light to interfere constructively or destructively.
- Locate the bright and dark fringes of Young’s double-slit experiment.
- Find the intensity at any point in the double-slit pattern using phasor addition.
- Analyze interference in thin films, accounting for reflection phase shifts, including soap films and anti-reflection coatings.
- Relate a mirror’s displacement in a Michelson interferometer to a countable number of fringes.
We will return to Young’s experiment, and its unsettling sequel with electrons, in the final problems.