Interference, Diffraction and Polarisation of Light Notes

Three experiments decided that light is a wave. Interference showed that two beams of light can add or cancel, diffraction showed that light bends round the edge of an obstacle, and polarisation showed that the wave is transverse, vibrating across the direction in which it travels. Isaac Newton had held that light is a stream of particles, but the wave picture of Christiaan Huygens, revived by Thomas Young in 1801 and completed by Augustin Fresnel, explained all three. Examiners ask this chapter as one phenomenon, one formula or one everyday example, so the names, the formulas and the examples have to be learnt as a set.

Interference of light

When two waves of the same frequency and a constant phase difference meet, the resultant intensity is greater than the sum in some places and almost zero in others. This redistribution of energy is interference; energy is never destroyed, only moved from the dark places to the bright ones. Thomas Young demonstrated it in 1801 by letting light from a single source pass through two close slits and fall on a screen, where alternate bright and dark bands called fringes appeared. Bright fringes occur where the path difference is a whole number of wavelengths, and dark fringes where it is an odd number of half wavelengths. The width of a fringe is given by the wavelength times the distance to the screen divided by the separation of the slits, so the fringes widen if the screen is moved back, if the slits are brought closer or if red light replaces blue. Sustained interference needs two coherent sources, that is sources with a constant phase difference, which is why a single source is always split in two instead of using two separate lamps. The colours of a soap bubble, of a thin film of oil on a wet road and of Newton's rings are everyday interference in thin films, produced between the light reflected from the top and the bottom surface of the film.

Diffraction of light

Diffraction is the bending of a wave round the edges of an obstacle or an aperture, with light spreading into the geometrical shadow. It becomes noticeable only when the obstacle or the slit is comparable in size with the wavelength. The wavelength of visible light is only about 400 to 700 nanometres, so light appears to travel in straight lines in ordinary rooms, while sound, whose wavelength is of the order of a metre, bends round a door easily and can be heard from the next room. In a single slit pattern the central bright band is the widest and brightest and the bands on either side fade; a diffraction grating splits white light into its colours, which is why the underside of a compact disc shows spectral colours. Diffraction also fixes the limit of what an instrument can separate: two point objects are just resolved when their angular separation equals 1.22 times the wavelength divided by the diameter of the aperture, so a telescope with a larger objective resolves finer detail and a microscope is improved by using light of shorter wavelength.

Polarisation of light

Ordinary light from a lamp or the sun vibrates in every plane perpendicular to its path and is called unpolarised. If the vibrations are confined to a single plane the light is plane polarised, and the device that does this, a sheet of aligned long-chain molecules, is called a Polaroid. Polarisation is possible only for transverse waves, so it is the proof that light is transverse and the reason sound, a longitudinal wave, can never be polarised. Malus's law gives the intensity passed by a second Polaroid as the incident intensity times the square of the cosine of the angle between the two, so crossed Polaroids at ninety degrees cut off the light. Light reflected from a surface is partly polarised, and at one particular angle of incidence, the polarising angle, the reflected light is completely plane polarised; Brewster's law states that the tangent of this angle equals the refractive index of the surface. Calcite and quartz split a ray into two polarised rays, an effect called double refraction and used in the Nicol prism. Scattered light is also polarised, which is why the blue of the sky is partly polarised.

Formulas to memorise

Where these effects are used

• Polaroid sunglasses and camera filters cut the glare reflected from water, glass and roads, because that reflected light is largely polarised in one plane.
• Liquid crystal displays in watches, calculators and screens work between two Polaroids.
• Three dimensional films are projected through Polaroids at right angles, so each eye receives its own image.
• Stress in a transparent model is studied by the coloured fringes it shows between Polaroids, a method called photoelasticity.
• Sugar solutions are tested in a polarimeter, because sugar rotates the plane of polarisation by an amount that depends on its concentration.
• Thin coatings on camera lenses use interference to cancel unwanted reflections.