Fresnel Biprism & Coherent Sources

Put two light bulbs side by side and their light overlaps everywhere, yet you never see a single fringe. Interference needs a special partnership between sources, and that partnership is rare.

The Fresnel biprism#

Fresnel found another way to make two sources from one. A biprism is two very thin prisms joined base to base. Their refracting angles are tiny, about half a degree, so it looks like a single glass plate with a barely raised ridge. A narrow slit S, lit by monochromatic light, is set parallel to the ridge.

Light through the upper half is bent slightly down; light through the lower half slightly up. To an observer beyond, the two beams seem to come from two virtual images of the slit, S₁ and S₂, very close together. Where the two cones of light overlap on a screen, fringes form, just as with two slits a distance d apart:

Coherent and incoherent sources#

Why ordinary sources are incoherent

In a lamp, a candle or the sun, light is emitted by atoms in separate bursts. An atom emits a short pulse lasting roughly 10⁻⁸ s (a wavetrain a few metres long), falls quiet, gets re-energized and emits again. Different atoms act independently, so each new wavetrain starts with a random phase.

With two lamps in place of the slits, the phase difference between them changes randomly millions of times a second. Fringes form and shift faster than any eye or instrument can follow, so we just see uniform light.

How a single slit fixes it

In Young’s experiment, a narrow first slit picks out light that reaches both slits from the same wavetrain. When the lamp emits a new wavetrain with a new random phase, the change reaches both slits at once, so their phase difference stays constant. The biprism works the same way: S₁ and S₂ are images of one slit.

Keep the path difference small

Wavetrains are only a few metres long, and in practice only a few centimetres of path difference can be tolerated. If one path is much longer, a wavetrain arriving by the short path meets a different wavetrain arriving by the long one, and the fixed phase relation is lost.

No light is perfectly monochromatic#

A perfect single wavelength would be a sine wave going on forever. A wavetrain of finite length is equivalent to a spread of sine waves of slightly different wavelengths: the shorter the wavetrain, the larger the spread. A sodium lamp gives two yellow lines, 589.0 nm and 589.6 nm, each spread by about ±0.01 nm.