Illustrated Physics
physics, drawn
Concept

Index matching — where it appears

Making two transparent materials have the same refractive index so that light crosses the boundary between them without reflecting or bending. It makes glass beads vanish in oil and is how optical filters built from powders select a single colour.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

How much darker a surface looks under a film of water. The diffuse reflectance of a surface covered by a thin film of clear water (solid), against its reflectance dry, with the dry value for comparison (dashed): (1 − Rₑₓₜ) a (1 − Rᵢₙₜ)/(1 − a Rᵢₙₜ), where the film traps and returns light that falls outside its escape cone. A bright surface of reflectance 0.9 falls to 0.77; a mid-grey one of 0.5 to 0.32, 64 per cent of its dry value; a dark one of 0.2 to 0.11, 54 per cent. Dark surfaces darken proportionally most, because each return trip costs them most; and a coloured surface grows more saturated, because the colours it absorbs are absorbed again on every return while the colour it reflects survives.

The sand that darkens when it is wet

Wet sand is darker than dry sand, a wet stone darker than a dry one, a splashed pavement darker in patches, and a wet white shirt turns grey and then see-through. Water is clear and absorbs almost nothing, so it cannot be adding darkness. What it does is change where the light goes. A film of water on a surface traps light that has been scattered back up, returning most of it for another chance to be absorbed. Water in the pores between grains replaces air with something closer to the grains' own refractive index, so each grain turns light aside less, and light wanders deeper before it gets out. Both lengthen the path, and on a longer path more light is absorbed by the material that was there all along.

optics · Scattering A filter made of glass powder and oil. The fraction of light transmitted straight through a 5 mm layer of N-BK7 grains packed to half its volume in the matching liquid, against wavelength, for grains of radius 5, 10 and 20 μm, from van de Hulst's extinction for large, weakly refracting particles. At the crossing the grains vanish and the layer is clear. A few tens of nanometres away each grain shifts the light passing through it in phase by enough to scatter a little of it out of the beam, and a thousand grains in a row scatter all of it: the passband is 51.7 nm wide at half height for 5 μm grains, 36.3 nm for 10 μm, 25.5 nm for 20 μm. Larger grains make a narrower filter, because the phase a grain imposes grows with its size; the same mismatch of index that a fine powder lets through, a coarse one scatters.

The colour at which glass disappears

Lower a glass rod into an oil of the same refractive index and it vanishes, except for a faint coloured outline. The outline is the clue. Glass and oil disperse light differently, so their indices can agree at only one wavelength; at every other the glass is still there, bending and scattering a little. Grind the glass to powder and pack it in the oil, and the mixture is clear at that one wavelength and opaque at the rest — a colour filter made of nothing but two transparent materials, whose colour moves by a whole hue for a few degrees of warming.

optics · Dispersion

Named alongside it

The objects these essays reach for when they reach for this one.

Refractive indexAbbe numberAbsorptionAlbedoDispersionEscape coneExtinctionFresnel reflectionKubelka munkMultiple scatteringOptical filterScattering

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