Com­ment & Anal­y­sis


BBC Earth (Asia) - - Contents - Dr He­len Cz­er­ski is a physi­cist and BBC sci­ence pre­sen­ter. Her book, The Storm In A Teacup, is out now

He­len Cz­erki on caus­tics

Proper sum­mer has fi­nally ar­rived, along with the op­por­tu­nity for sit­ting out­side and bask­ing like a lizard through long and lazy af­ter­noons. On a sunny day, while eat­ing al fresco, in­tense sun­light glints off plates and glasses, and the most im­por­tant ques­tion of the af­ter­noon is whether clot­ted cream or jam should be spread on scones first. But take a mo­ment away from th­ese pon­der­ings to look at the ta­ble – re­ally look – and you’ll see that it’s cov­ered in bright lines and odd dark patches. The sur­face of your tea is dec­o­rated with two sharp semi­cir­cles on the side fur­thest from the Sun. Your trans­par­ent glass of wa­ter casts a weird dark shadow (even though it is trans­par­ent), cut in half with a blaze of white light. Inside the rim of a plate, there are thread-like lines which roll across the sur­face as you tilt it. All of th­ese fea­tures are called caus­tics, and a sunny day of­fers the per­fect op­por­tu­nity to ad­mire them.

Caus­tics are the sharp di­vid­ing lines be­tween bright and dark re­gions, and they turn up wher­ever par­al­lel light rays meet curved sur­faces. Be­cause the Sun is ef­fec­tively a point source a long way away, the light rays com­ing from it are al­most per­fectly par­al­lel. When they reach the inside of a teacup, they bounce off at dif­fer­ent an­gles, de­pend­ing on which part of the inside of the cup they hit. But there are some re­gions that many dif­fer­ent rays get directed to (those are the bright semi­cir­cles) and some re­gions which are ef­fec­tively for­bid­den – they can’t be reached by any re­flected ray. In your cup, the two in­tense semi­cir­cles meet at a point called the cusp, which makes a dis­tinc­tive pat­tern known as a nephroid caus­tic, be­cause it’s vaguely kid­ney-shaped.

You’ve prob­a­bly also seen caus­tics on the bot­tom of a swim­ming pool, where waves trav­el­ling across the sur­face fo­cus light into criss-cross­ing bands, and di­rect it away from the spa­ces in be­tween. The sur­face where you see a caus­tic is act­ing like a screen, giv­ing you a sneak peek into where light was trav­el­ling. If you move the screen, you’ll see the pat­tern change, but the three-di­men­sional pat­tern it­self was there all along. The light field around us is lumpy and bumpy like this all the time, espe­cially on sunny days. But we need to put an ob­sta­cle in the way to make the lumps and bumps vis­i­ble.

The fi­nal stage in the beauty of caus­tics brings us to the rain­bow. Light paths are bent as they cross from one trans­par­ent ob­ject to the next, vi­o­let bends more than red. You may well see some coloured lines in the shadow from your wa­ter glass be­cause each colour gen­er­ates its own caus­tic, and they don’t line up. And so we come to the search for a pot of gold. A rain­bow is formed as light from the Sun re­flects and re­fracts its way around the inside of tiny wa­ter droplets in the sky. Af­ter­wards, the light field for each colour is lumpy, with caus­tics di­vid­ing the most and least in­tense re­gions. You in­ter­cept that pat­tern with your own eyes, and you see the rain­bow – dif­fer­ent caus­tics for red, or­ange, yel­low, green, blue, indigo and vi­o­let, glit­ter­ing in a gi­ant arc across the sky. The lumpy light field ex­ists at ev­ery point be­tween you and those wa­ter droplets, and your eyes de­tect the unique pat­tern at your view­point. But this means the pot of gold at the end of the rain­bow is unattain­able, be­cause all that’s there is a three-di­men­sional pat­tern. How­ever, the dish of but­ter on the ta­ble is right here, so maybe I’ll ad­mire the caus­tics inside the dish and make do with that in­stead.

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