Of Particular Significance

# Chapter 6, Endnote 7

• Quote: Cells can be photographed using a microscope. That won’t work for atoms, so tiny that visible light can’t bounce off them effectively.

• Endnote: Visible light’s waves have crests and troughs much wider than atoms, so a flash of visible light can no more reflect off a single atom than ocean waves can reflect off a pebble.

In addition to a frequency, simple waves have a wavelength (the distance between one crest and the next). If light with a certain wavelength is used to illuminate an object, details of that object that are smaller than the light’s wavelength cannot be observed.

The basic idea is this. Imagine you send light (or any other wave) through a screen with a very small pinhole in it, smaller in diameter than the wavelength of the light. You then try to observe the waves that pass through the hole to determine the size of the hole. What you will find is that the waves form a circular structure, known as an Airy disk (here’s an image), whose width is determined by a combination of the hole’s size and the wavelength of the waves. If the wavelength is much longer than the diameter of the hole, this disk will be completely spread out and not observable.

The same would apply if there were two small pinholes very close together; you would not be able to tell clearly that there are two holes rather than one if the distance between the holes were small compared to the wavelength of the light. That’s because each hole’s Airy disk would be larger than the distance between the holes, and so they would overlap, making it impossible to see that there are really two Airy disks rather than a smeared out single disk.

Small objects, rather than small holes, behave in more or less the same way, as in the example given in the endnote of a pebble impacted by ocean waves. Whatever small effect one pebble has on the shape of an ocean wave that scatters off it, it won’t be much different from the effect of two pebbles of half the size placed close together. That makes it impossible to use the waves to infer the location and size of the pebbles.

In the same way, our eyes (or computers) cannot infer the shapes and locations of atoms using waves of visible light, whose wavelengths are thousands of times larger than the sizes of atoms and the typical distances between them.

The technical formulas behind this are found in physics textbooks and on various websites, such as this one.

Search

## Recent Posts

Got a question? Ask it here.