Brocken Dreams
spectres, spectra and weird optical effects [1800 words plus Physics, 10 min
Do the beauties of the Universe lose it when you explain the science-y stuff? Or does the physics make it all even wonderfuller?
Dank and miserable it was all the way up Ben Lomond on that late December morning. Disappointing: especially as we have along, on her very first Scottish mountain, my son’s girlfriend from the southern United States. But then, as we reach the upper moorland, the mist starts to move around us like ghosts of the afterworld sulkily becoming aware of these intrusive humans. A few more steps and the air brightens, grey-black to grey to sudden blue: and we’re above the cloud, in sparkling sunlight and subzero air, with 10 centimetres of hoar-frost crunching underfoot.
This is a long post with several diagrams, which may overflow the end of your email. If suddenly cut off, return to the top here and hit ‘view in browser’ at top right.
The north-east hollow of Ben Lomond traps the warm, moist air, swirling it around like long-suffering youth-hostel soup. Coming down the sharp northwest ridgeline in the sunshine, that swirl of mist is on our right. So that when the Brocken Spectre appears in all its glory, I simply turn half-right and snap its photo.
In fact, this ridge of Ben Lomond is one of only two places where I’ve met the Spectre twice over, on two separate occasions.1
The spectre is named after the Brocken, which is the high point of the Harz Mountains of northern Germany. (It's 1141m high if you don't count the red-and-white striped radio tower, which adds a further 123m.) The poet Coleridge, as it chanced, climbed the Brocken in 1799. He records that the ghostly figure of yourself that you see in the clouds carries, if you look very closely, a notice with the names of all those who have cursed you with "May you be carried to the top of the Brocken" – this considered by Germans of 1799 as a bad place to be.
Almost everybody who meets the spectre recognises it for what it is: a shadow cast upon the cloud. For one thing, when you wave at it, it waves back. Because the shadow is cast on water drops at many different distances, it's only coherent when looking directly down the sunbeams. So you only see your own shadow, and any companion standing right beside you – but it's your own shadow that has the wide, multicoloured halo called the Glory.
A mountain riddle: what's the Brocken Spectre doing in the photo?2
Mysteries of the Electromagnetic Theory
The Glory is one of the most complicated bits of optics. Even its more cheerful cousin the rainbow isn’t all that simple. Rainbows involve refraction and reflection, as understood by Isaac Newton in 1704. If you did Physics O-level, you may have seen an explanatory diagram in terms of light-rays:
Light-rays are bent (refracted) as they pass from air into water, with light at the blue end of the spectrum being bent rather more. The light rays then bounce (reflected) off the back surface of the raindrop, and get refracted again on their way out of the raindrop.
The rainbow circle has red on the outside, and has a radius of 42° centred on the point directly opposite the sun.
This is all very science-y and mathematical, with those Greek letters for the angles and Snell’s Law of refraction being applied at the interface. However, if you happen to have a physics-type mind, you might have a question or two. Like, what if the light-ray doesn’t happen to hit the raindrop roughly two-thirds of the way up from the centre-line?
Getting technical, that diagram up there is what science types describe as “er, – wrong actually”. Another diagram from Wikipedia shows what actually happens to red rays hitting the raindrop:
So that a red-only rainbow would look a bit like the picture I’ve faked up in Photoshop, with a strong red at the outside edge, but a whole lot of fainter rays scattered all over the inside of the arc.
Now apply a slightly smaller orange just inside the red, a yellow just inside the orange, and so on, to get the proper rainbow effect. The all-colours of light scattered on the inside combine together into white, so that the sky inside the rainbow arc will look brighter than it does outside it.
Well that’s a bit of physics from 1704. Light doesn’t actually consist of rays shooting out of the sun in straight lines like water from a high-pressure hose. And so, if you look just inside the rainbow, you may sometimes spot a ‘supernumary rainbow’ – alternating bands of orange and mauve. If you don’t spot it, that’s because the raindrops involved happened not to be of uniform size and around 1mm wide. If you do spot them, though, then your physics has just jumped forward to 1804, and the wave nature of light…
Supposing you should be ready to plunge forward into the modern ideology of the early 1800s… You could consider the light-rays emerging from the raindrop just inside the arc of the rainbow: let’s say, at 39° from the centre point rather than the full 42°.
There are two possible paths through the raindrop to emerge at that angle: one just above the 42° sweet-spot, and one just below. The outer path is very slightly longer than the inside one. If that difference comes to exactly half a wave-length of this purple light, then the two rays will cancel each other out: with no violet in it, the light you’ll see coming back around this 39° arc will be greenish. Whereas slightly inside or outside the 39° arc, it’s the greenish colours that get cancelled out, to leave a band of violet.3
Glory, glory
Rainbows involve refraction and reflection, as understood by Isaac Newton. Supernumerary rainbows include the waveform effect of interference. Indeed, these supernumerary rainbows were the crucial evidence for lightwaves (Thomas Young, exactly a century later, in 1804).
The Glory is something else.
It only forms when the cloud droplets are of uniform size: and that size must be just a few wavelengths of light – which is to say just a few microns, or thousandths of a millimetre. Explaining it involves something called the ‘surface wave’, whereby the light wanders along the air/water interface for a while before emerging: with any further details provided by what’s described in one text-book as ‘scientific arm-waving’: “In some way light is backscattered after traversing the periphery of droplet. Examined in detail, each drop is found to shine uniformly around its edge with an annulus of light that is coherent (the waves are in phase).”
The colours of the glory can, however, be derived mathematically from James Clerk Maxwell's four equations of electromagnetism. If you feed those four equations – among the most elegant in all physics – into a computer, it can calculate and display the glory for any given size of cloud droplets. The human mind can’t really ‘understand’ glories, but the computer can!4
If the cloud droplets are 20 microns wide, the inner red ring of the glory will be 5° across, which is roughly the length of your thumb when held at arm’s length. As the drops get smaller, the rings get bigger: droplets of 10 microns give an inner red ring of 8°, the length of your index finger.
Foggy foggy dew
In April 2016 I slept on top of one of Scotland’s least interesting hills: the flat grassland summit of A’ Bhuidheanach Bheag (the small yellowish thing) above Dalwhinnie.
Mist gathered in the glen, then swelled gently up the peaty slopes, to level off at the 850m contour. Given that I was lying at the 890m contour this was a highly satisfactory state of affairs. On a swelling of the moor, 100 red deer stood outlined against the grey-white background. And as I dipped into the top of the fog, a wide white arch rose above me. It was yet another Optical Effect, the fogbow.
When raindrops are really big, like 1mm or more, you get a rainbow. When they’re really tiny, like the wavelength of light, you get a glory. In-between sizes, and you end up with the fogbow.
Here’s one at the Commando Memorial at the bottom of Ben Nevis. And here’s the most famous one in all mountaineering: as seen by Edward Whymper on his way down the Matterhorn, on the 14 July 1865.
When lo! a mightly arch appeared, rising above the Lyskamm high into the sky. Pale, colourless and noiseless, but perfectly sharp and defined, except where it was lost in the clouds, this unearthly apparition seemed like a vision from another world, and almost appalled we watched with amazement the gradual development of two vast crosses, one on either side.
… it was a fearful and wonderful sight, unique in my experience, and impressive beyond description, coming at such a moment.
In a footnote he describes it as a fog-bow, and admits that his engraving may, under the traumatic circumstances, not be accurate – he and his two guides were the only survivors of the party of seven that set off up the mountain fourteen hours before.
My heart leaps up when I behold
A rainbow in the sky:
So was it when my life began;
So is it now I am a man;
So be it when I shall grow old,
Or let me die!
Get lucky enough to see any of these optical phenomena (or phenomenons, but please not phenomenas) – and if it doesn’t make you feel just ever-so excited – well, it’s time to be dead.
Harsh words from William Wordsworth. But not, I think, unfair.
The other being Halls Fell of Blencathra, Lake District
Since the spectre reflects the person throwing the shadow, the Brocken has to be just taking a photo of the human being. As its photo’s being taken straight into the sun, it’s not going to come out very well.
Supposing you should want to advance into the mid-20th century – which you don’t. Light isn’t rays and it isn’t waves either. The two magenta arrows in my diagram represent two possible paths through the raindrop of a single photon. Two paths which, because of the phase difference derived from its wavelike nature, cancel each other out, so that there is zero probability of the purple photon emerging in this particular direction.
The way it’s done is via ‘Mie scattering theory’. The basic technique is that, at any point on its path, the lightwave is considered as setting out promiscuously in every possible direction: but due to interference (as in that secondary rainbow) the promiscuous overlapping lightwaves cancel each other out in every direction except carrying on forwards in a straight line. No, it doesn’t make sense to me either. But it works.
Science enhances wonder, but only if we resist allowing it to enframe us. Even when we can explain the Spectre through scientific principles, this should not diminish our first hand human experience of its beauty or its symbolic resonance. On the contrary, the scientific explanation itself can inspire wonder, as it reveals the profound, unchanging laws of the universe through a different symbolic language. Both forms of symbol and consequent wonder draw us to consider the atemporal aspects of Being, and the Ground upon which it, and we, depend.
Air like '...long-suffering youth-hostel soup.' Haha.
Fascinating! I'd never heard of a fogbow before.