Tag: wave optics

What it takes to wash a strainer: soap, water and some wave optics

When I stay over at a friend’s place whenever I come to Delhi, I try to help around the house. But more often than not, I just do the dishes – often a lot of dishes. One item I’ve always had trouble cleaning is the strainer, whether a small tea strainer or a large but fine sieve, because I can never tell if the multicoloured sheen I’m seeing on the wires is a patch of oil, liquid soap or something else. The fundamental problem is that these items are susceptible to the quirks of the wave of nature of light, as a result of which their surfaces display an effect called goniochromism, also known as iridescence.

At first (and over 12 years after high school), I suspected the wires on the sieve were acting as a diffraction grating. This is a structure that has a series of fine and closely spaced ridges on the surface. When a wave of light strikes this surface, the ridges scatter different parts of the wave in different directions. When these waves interact with each other on the other side, they interfere with each other constructively or destructively. A constructive interference produces a brighter band of colour; a destructive interference produces a darker band. How the wave becomes scattered is a function of its frequency: the lower the frequency (or redder the colour), the more the wave is bent around a grating.

As a result, white and continuous light appears to breakdown into its constituent colours when passed through a diffraction grating. But it must be noted that a useful diffraction grating used in a visible-light experiment has something like 4,000-6,000 ridges every centimetre. The width of each ridge has to be of comparable size to the wavelength of visible light because only then can it scatter that portion of light. On the other hand, the sieve I was holding appeared to have only 6-8 ridges every centimetre, so the structure itself couldn’t have been what was effecting the sheen.

Goniochromism, or iridescence, is caused when two transparent or semi-transparent films – like liquid soap atop water – reflect the incident light multiple times. In fact, this is one type of iridescence, called thin-film interference. Here, imagine a thin layer of soap on the surface of a thin layer of water, itself sitting on the surface of a vessel you’re cleaning. (With a strainer, the water-soap liquid forms meniscuses between the wires.) When white light strikes the soap layer, some of it is reflected our and some is transmitted. The transmitted portion than strikes the surface of the water layer: some of it is sent through while the rest is reflected back out.

When the light reflected by each of the two layers interact, their respective waves can interfere either constructively or destructively. Depending on the angle at which you’re viewing the vessel, bright and dark bands of light will be visible. Additionally, the thickness of the soap film also decides which frequencies are intensified and which become subdued in this process. The total effect is for you to see rainbow-esque pattern of undulating brightness on the vessel.

So herein lies the rub. Either effect, although the second more than the first, produces what effectively looks like an oily sheen on the strainer in my hand no matter how many times I scrub it with soap and run it under the water. And ultimately, I end up doing a very thorough job of it if there was no oil on the strainer to begin with – or a very bad one if there was oil on it but I’ve let it be assuming it’s soap residue. It’s a toss-up… so I think I’ll just follow my friend C.S.R.S’s words: “Just rub it a few times and leave it.”

Featured image credit: Lumix/pixabay.

What is VLBI?

On June 25, scientists announced the discovery of a trio of supermassive black holes at the center of a galaxy 4.2 billion light years away. The find was credited to the European VLBI Network. A Space.com report stated that this network “could see details 50 times finer than is possible with the Hubble Space Telescope”. How is this achieved?

VLBI stands for Very-Long-Baseline Interferometry. It is a technique used in astrometry to obtain high resolution images of the sky using a network of telescopes instead of using one big telescope. VLBI is commonly used to image distant cosmic radio sources such as quasars.

This sophisticated technique has its roots in 18th century physics, specifically in Thomas Young’s famous double-slit interference experiment in the early 1800s. When Young placed a screen with two extremely narrow slits in front of a light source, such as a burning candle, the shadow cast on the other side was actually an alternating patchwork of bright and dull bands. This was the interference pattern. Young’s experiment was important to establish that light travels as a wave, overturning Newton’s conviction that light was composed of particles.

The interference pattern

When light passes through each slit, it diffracts, i.e. starts to spread out. At some point in front of the slits, the diffracted waves meet and interfere. Where crest met crest, there was constructive interference and that resulted in a bright band. Where crest met trough, there was a duller band. Where trough met trough, there was a dark band. If the position of the slits was changed, the interference pattern also shifted.

In VLBI, the candle is replaced by a distant source of radio waves, like a quasar. The slits are replaced by radio antennae on telescopes. Since the Earth is rotating, the antenna are in relative motion with the quasar. As a result, there is an interference between the signals being received by the two telescopes. This interference pattern is processed at a central location along with the time at which each signal was received at each antenna as recorded by a clock.

In the second stage of this colossal Young’s experiment, let’s talk some wave physics. Radio waves have greater wavelength than visible light. As a result, radio telescopes have an inherently low angular resolution than optical telescopes of the same size. Angular resolution is defined as the ratio of an emission’s wavelength to the diameter of the telescope receiving it. Qualitatively, it describes the smallest unit of distance the telescope can distinguish in the image it receives and that must be as low as possible. For example, a 50-meter wide radio telescope will have an angular resolution of 50/0.01 = ~41.2 arc-second. An optical telescope of the same size will have an angular resolution of 0.004 arc-second, 10,000-times better.

Baseline + Atomic clocks

VLBI resolves this issue (this isn’t really a pun). Because there are multiple telescopes receiving the radio signals, the angular resolution is redefined: it’s no longer the ratio between the wavelength and the diameter of the telescope. It’s the ratio between the wavelength and the baseline. The baseline is the maximum physical separation between two telescopes in the array. If, say, the baseline is 1,000 km, the angular resolution of an array of radio telescopes becomes 0.002 arc-second, 20,000-times better.

However, this technique couldn’t find wide implementation until the atomic clock was invented in the 1950s. Before they were around, a single metronome had to be connected to multiple telescopes with cables, which limited the baseline length. With atomic clocks, telescopes could be placed on different continents because the clocks were globally coordinated.

So, a telescope receives a radio signal, a computer sticks a timestamp on it and sends it to the receiver. The receiver collates such data from different telescopes and creates the fringe pattern characteristic of interference. A processor finally recreates the source of all the radio waves at different locations using the fringe pattern and the times at which each signal was received. Of course, there are many systems in between to stabilize and improve the quality of the signal, to coordinate observations by the telescopes, etc., but the basic principle is the same as in Young’s experiment of two centuries ago.