Physical Optics and Gravitational Waves

Waves do not collide and bounce off each other. They pass straight through, and where they overlap the displacements simply add. Two crests meeting give a bigger crest; a crest meeting a trough cancels.

Where the result is larger the waves are said to interfere constructively; where they cancel, destructively. Which happens depends on the path difference — how much further one wave has travelled than the other.

A path difference of a whole number of wavelengths means the waves arrive in step and reinforce. A path difference of an odd number of half-wavelengths means they arrive exactly out of step and cancel.

For a stable pattern the sources must be coherent: the same frequency and a constant phase difference. Two separate light bulbs are not coherent, because each emits in random bursts, so no pattern is seen. This is why Young's experiment splits light from one source into two rather than using two lamps.

λ

wavelengthm

n

order

Two waves drawn separately, then added. Slide the phase difference to 0° and the resultant is twice the height; slide it to 180° and it flattens to nothing. Everything in interference is that one picture, applied to light.

Light through two narrow, closely spaced slits produces a pattern of bright and dark fringes on a distant screen. That is not something a particle model can explain, and it is the classic demonstration that light travels as a wave.

Each slit acts as a source. At the centre of the screen the two paths are equal, so the waves arrive in step and there is a bright fringe. Move to one side and one path grows longer than the other; when the difference reaches half a wavelength the waves cancel and there is a dark fringe; at a whole wavelength they reinforce again.

The spacing between fringes depends on the wavelength, the slit separation and the distance to the screen. It follows that red light gives wider fringes than blue, since red has the longer wavelength — and that using white light produces a white central fringe with coloured fringes either side, because each colour has its own spacing.

The fringes are very close together, which is why the slits must be narrow and close and the screen far away. That is also why the effect is not obvious in daily life.

λ

wavelengthm

a

slit separationm

x

fringe spacingm

D

slit-to-screen distancem

Diffraction is the spreading of a wave as it passes an edge or through a gap. The narrower the gap, the more the wave spreads, and the effect is greatest when the gap is about the same size as the wavelength.

This is why sound bends round a doorway and light does not: sound wavelengths are metres, comparable to a doorway, while visible light is around half a micrometre.

A diffraction grating has thousands of slits per centimetre rather than two. Many slits mean the bright fringes become very sharp and widely separated, which makes measurement far more precise than with a double slit.

Because the angle of each maximum depends on wavelength, a grating splits white light into a spectrum — and unlike a prism it does so by a calculable amount. That is why gratings are used in spectrometers to identify the elements in a star from the light it emits.

d

spacing between slitsm

θ

angle of the maximum°

n

order

N

lines per metrem⁻¹

Light is a transverse wave, and the vibrations of an unpolarised beam happen in every direction perpendicular to the direction of travel. A polarising filter transmits only those vibrating in one plane, and the light that gets through is plane polarised.

Because only transverse waves can be polarised, the fact that light can be is direct evidence that it is transverse. Sound cannot be polarised, and that alone tells us sound is longitudinal.

Put two polarising filters in line and rotate one. At parallel orientation most light passes; at right angles almost none does. This is how polarising sunglasses cut glare: light reflected from water or a road is partly polarised horizontally, so a filter oriented vertically blocks it.

The same principle appears in photography, in stress analysis of transparent models, and in liquid crystal displays.

Einstein's general relativity describes gravity not as a force but as a curvature of spacetime. A consequence, predicted in 1916, is that violently accelerating masses should send ripples through spacetime itself — gravitational waves, travelling at the speed of light.

They are extraordinarily weak. A passing wave stretches space in one direction and squeezes it in the perpendicular direction, but by a fraction of about 10⁻²¹ — less than a thousandth of the width of a proton across a four-kilometre detector.

LIGO detects them with a laser interferometer built on exactly the interference principle earlier in this chapter. A laser beam is split down two perpendicular arms, reflected, and recombined. Normally the two paths cancel. A passing gravitational wave changes one arm's length relative to the other by a minute amount, the cancellation is no longer perfect, and light appears at the detector.

The first detection was in September 2015, from two black holes of about 29 and 36 solar masses merging over a billion light-years away. It confirmed a century-old prediction and opened a way of observing the universe that does not rely on light at all — which matters, because events like black hole mergers emit almost no light.

When two waves of the same frequency travel in opposite directions through each other — usually an incident wave and its own reflection — they superpose into a pattern that does not travel at all. Certain points never move, and others oscillate with maximum amplitude, and neither set changes position.

The points that never move are nodes, where the two waves are permanently out of phase and cancel. Between them are antinodes, where they are permanently in phase and reinforce. The distance from one node to the next is half a wavelength, which is the fact nearly every calculation rests on.