Virtual Recreation of Newton’s ‘Experimentum Crucis’ Two Prism Experiment

Dispersion of light through two prisms rendered in Luxrender

Well, a virtual recreation with a bit of license. This started as a test to see if the physically based render program Luxrender  can make a believable simulation of white light passing through a prism.  Unbiased render engines like Luxrender send out very many virtual photons and calculate their paths according to physical laws, and as the ray-tracing algorithm includes colour dispersion, it should work in theory.

Throw a second prism into the scene, and we have Isaac Newton’s ‘Experimentum Crucis’: one of a series of experiments performed by Newton in 1666 and reported in a letter to the Royal Society in 1671 (1), showing how white light is composed of a range of colours separable by a prism.  He demonstrated the colours were a property of the light, not the prism, by using a slit to isolate an individual colour from one prism, and passing it through a second where no further separation of colours occurred – the second prism just refracted the single colour to one side.  Here is Newton’s own drawing of his two-prism experiment.

Experimentum Crucis
Experimentum Crucis

My distances and prism sizes are not accurate, but the simulation still works.   Also, while Newton used the sun as a light source, sometimes passed through a slit before the first prism or focused through a lens as above, my source is a small rectangular surface radiating in all forward directions, but with a collimating tunnel placed in front of it.  If the light source is too ill-defined or unfocused, in both reality and in the simulation, the separation in the spectrum can look reasonable superficially, but actually comprise a series of fuzzy overlapping spectra.   The result being, when I ran this without the collimator, the green band split into further discernible colours.   That said, it’s worth remembering that while Newton reported seeing seven colours, the actual spectrum is a continuum of wavelengths, so a single colour will in fact be made of a range of further dispersible shades – we just don’t discern it.

Here is a close-up of the isolating slit and the green spectral ‘line’ deviated but not dispersed by the second prism.  I’ve also in this picture turned out the background light used solely for dramatic effect in the first picture.

Dispersion through two prisms

And here are wireframe pics of the layout (scene created in Poser and linked to Luxrender via Reality):

Screen-Shot-2014-06-16-at-01.43

Screen-Shot-2014-06-16-at-01.52

Screen-Shot-2014-06-21-at-03.15

An interesting feature of this type of modelling is the need for a so-called Tone Mapping process, by which the multiple wavelengths for which the ray-tracing maths must be repeated to simulate dispersion is translated into the red, blue, and green (RGB) that the computer monitor can understand to display the result.

Also worth noting the limitations to this sort of progam as a virtual optical bench.  Luxrender is not, for example, up to calculating the quantum probability amplitudes necessary to simulate interference as seen in the double slit experiment.

 

References

(1)  doi: 10.1098/rstl.1671.0072 Phil. Trans. 1 January 1671 vol. 6 no. 69-80 3075-3087   (link to Royal Society Publishing)

Also of interest:

Experimentum Crucis
J. A. Lohne
Notes and Records of the Royal Society of London, Vol. 23, No. 2 (Dec., 1968), pp. 169-199
Published by: The Royal Society

To Catch a Humming Bird

Humming Bird ©Tim Jones

It’s no secret humming birds beat their wings fast, but it’s also nice to catch one in the act.

I snapped this Allen’s Hummingbird (Selaphorus sasin) yesterday at a shutter speed of 1/800th second (0.00125 s) and his wings are still a blur.

Humming birds can beat their wings at up to 200 beats per second – the wing completing its travel in 0.005 s.  I reckon the blurred area above represents about a quarter of a full beat, which is just what we’d expect if this guy were flapping near the max. (i.e. 4 x 0.00125 = 0.005).

Look how the body stays almost perfectly still; it reminds me of those stories about being able to balance a coin on the bonnet of a Rolls-Royce.  There is a slight wobble: if you compare his head to his foot (and the pictures below where he’s settled down) the head shows a slight shimmer.

With the sun catching him like that, we’re also getting a good demonstration of the iridescent color effects humming birds exhibit due to interference of light within the microstructure of their feathers.

Here are a few more pictures of the same bird:

Humming Bird ©Tim Jones

Humming Bird ©Tim Jones

Humming Bird ©Tim Jones

 

 

Unexpected Space in a Pasadena Parking Garage

You never know what unexpected quirky stuff is going to show up if you keep your eyes open.

Graffiti by Kenny Scharf in garage of Pasadena Museum of California Art (Photo:Tim Jones)
Graffiti by Kenny Scharf in garage of Pasadena Museum of California Art (Photo:Tim Jones)

This afternoon, Erin and I visited the Pasadena Museum of California Art to see an exhibition of works by Edgar Payne.  We’re both fans of American plein-air painting, and Payne was a master of the technique – so the exhibition was a great success.  But parking up, we found the Museum’s garage had its own artistic charm.

Graffiti by Kenny Scharf in garage of Pasadena Museum of California Art (Photo:Tim Jones)

The graffiti is by artist Kenny Scharf, and instantly caught my eye with its images of rocket ships and swirling galaxies.   The garage – or Kosmic Kavern – is the colorful legacy of an exhibition of Scharf’s work in the gallery proper in 2004 – his graffiti in the garage was just never cleaned off!  Scharf’s work is influenced by the 1962 animated comedy sit-com The Jetsons, and there are other bits of space and nuclear iconography from the Golden Age of American Science spotted around – like the mushroom cloud and atom-swirl.

The Jetson's lived the future for folks in 1962 (Photo:Tim Jones)
The Jetson’s lived the future for folks in 1962
The Jetsons (Wikipedia)
The Jetsons (Source: Wikipedia)

Some of the Jetson’s techno-utopia became a reality.  But not, unfortunately, the aerocar or three-day week.

 

More Kenny Scharf

If you’d like to see more of his Kenny Scharf’s work, there’s a good collection at Artsy’s Kenny Scharf Page

 

Of related interest on Zoonomian

Chemistry in the Golden Age of American Science

Buck Rogers – A Copper-clad Lesson from History

Orderly Animals

Gee, humans are smart.  Never mind the moon landing, today we have these fantastic slide-away pantries to squirrel our stuff away.  The ultimate in mall to wall storage efficiency.

Then again, maybe that honor should go to the first of two non-human tidy housekeepers that crossed my path this week: the Acorn Woodpecker (Melanenpes formicivorus):

I’ve written about woodpeckers before –  HERE.   But this example, snapped in Santa Barbara Zoo (of all places, given the birds are all over the area) is the best example of an acorn-saturated tree trunk I’ve seen.  Acorns placed by woodpeckers into holes excavated by woodpeckers – for later consumption.

 

Tidy Trashlines

Next up, the Trashline Orb Weaver spider (genus Cyclosa).  I came across this guy on a pick-your-own blueberry adventure at nearby Gaviota, strung across the bushes.  (And vulnerable to accidental picking –  it’s likely I ate one of these.):

Trashline Orb Weaver Spider
Blueberries
Trashline Orb Weaver Spider
Trashline Orb Weaver Spider

The spider is the darker lump at the center of the web, hidden among the string of five packages: its ‘trash’, made of bits of old victims, egg sacs, plant material and such like caught in the web.  I’d never seen one before, but now I now about them I’ve spotted a couple more in other locations.  Here’s one, startled to life below a vertical, albeit incipient, trashline:

Trashline Orb Weaver Spider

Left alone, they pull in their legs and try to look like a piece of trash:

Trashline Orb Weaver Spider
Trashline Orb Weaver Spider – legs tucked in

Incidentally, in the top picture you can see a visibly thicker, extra-strong, ‘cross-beam’ section of webbing, the stabilimetum, on which the main web and trashline hangs.

Why go to the trouble?   Spider researchers reckon the trashline disguises the spider from approaching food insects, which can then be grabbed more easily; but also hides it from predators ~ a strategy more effective against birds than wasps (ref 1).

Yeah, we’re smart – in some things; but we’re not the whole story by a long shot.

Of related interest

Decorative Spider Webs Attract Dinner‘ (BBC item from 20/9/12)

References and further reading

1. Detritus decorations of an Orb-Weaving spider (Cyclosa mulmelnensis): for food or camouflage ?  Tan E. & Li D., Journal of Experimental Biology, 2009, DOI 10.1242/jeb 030502 (pdf here)

2. Insectidentification.org

3. Trashiline Orb Weaver – A cool spider (abundantnature.com)

Photos copyright Tim Jones

Darwin’s Many Origins

Owning multiple copies of a book isn’t that unusual.   There’s that extra copy for the bath, the duplicate Christmas present you don’t have the heart to return, or maybe you’ve just made home with someone with similar interests – and library: always a good idea.  But no one has hundreds of copies of the same title – do  they?

Sure they do.  Meet the front end of the Huntington Library‘s 252 strong collection of Darwin’s Origin of Species –  all 20 feet of them. I snapped this at the permanent ‘Beautiful Science’ exhibition last month, and have just gotten around to a bit of research:

And turning the corner, here are the rest of them:

Henry Edwards Huntington acquired much of his collection, now at San Marino, by buying up ready-made collections or even whole libraries.  But some books he bought individually, including, in 1860s New York, an 1859 first edition of the Origin of Species in original cloth – for $22.79 (1).   Checking Abebooks.com just now, I see you can pick up the same thing in the same city today for a cool $210,000 (Arader Gallery). Nice investment, Henry.

All the Origins at Huntington are different.  Most of the variations are reprints of the early six editions published by John Murray between 1859 and 1872; and then there are all the various languages.  The original six do vary in content though, with Darwin making material changes in response to readers’ comments.

Despite the title’s legendary status, the print runs of Murray’s Origin look modest by modern standards:

1st Edition (1859) 1,250

2nd Edition (1860) 3,000

3rd Edition (1861) 2,000

4th Edition (1866) 1,500

5th Edition (1869) 2,000

6th Edition (1872) 3,000

which goes some way to explain their value today  – although the first editions command disproportionately very much more than any of the others.  (For a comprehensive bibliography of all Darwin’s works see Freeman, R. B. 1977. The works of Charles Darwin: an annotated bibliographical handlist. 2d ed. Dawson: Folkstone. and accompanying database at Darwin Online.)

Scholars have argued over the Origin’s scientific content since, well, its origin – so it’s refreshing to find an analysis along a different tack, like Michele and Chris Kohler’s essay about the Origin of Species as a physical object (2).

The authors mention Huntington’s collection of Origins as one of the three largest, along with the Kohler Collection at the Natural History Museum London and the Thomas Fisher Library of the University of Toronto.

Their research also suggests that many more people may have read the first edition than the 1,250 figure suggests, with 500 copies going not to wealthy individuals (books like this were still a luxury for most people) but to Mudies Lending Library – the largest commercial library in the country.  (btw, current Origin sales are a respectable 75,000 to 100,000 units per annum.)

There’s also a discussion on how the content was on occasion not so much lost, but subtley changed, in translation, as in the case of Heinrich Bronn’s first German edition.

The Kohlers’ analysis of price history shows a run-away escalation of first edition values in the 20th and 21st centuries: so from an average £36 in the mid-50’s, to still only £4000 in the 80’s, to a top price of £49,000 in 1999; that’s still a long way off the £100,000+ values being achieved today.

The collector demographic has necessarly changed in step: from pure scholars to business people; but perhaps those working in sci-tech related areas who want, and can afford, to be close to a piece of scientific history.  Maybe that ownership requires a Henry Huntington income is a good thing – reflecting an increased awareness of the value of it’s intellectual message?

There again, maybe it’s all going the way of the art market, with rare books becoming a commodity currency.  What do you think?

References

1. Henry Edwards Huntington, A Biography. James Ernest Thorpe, University of California Press, 1994

2. Essay by Michele and Chris Kohler in: The Cambridge Companion to the Origin of Species, Ed. Michael Ruse, Robert J Richards, New York, 2008 (Archive.org .txt version here)

 

 

 

Something’s Brewing in Darkest Surrey

Wine fermenting in a demijohn (photo: Tim Jones)

Q – What did the grape say when an elephant stepped on him?

A – Nothing.  He just let out a little wine.

The first alcohol I ever drank was home brewed.  I was twelve when the evil liquor – orange and raison wine – was served up by my refreshingly enlightened policeman uncle of all people.  We’d visit the house and find these wort-filled vessels in the bathroom, glug-glug-glugging as bubbles of carbon dioxide chugged through little glass airlocks.

Not that I was swilling the stuff in quantity you understand, but what better introduction to the practical application of biochemistry and chemical engineering.  Who knows what influence these little episodes have on later life decisions?

Six years later, as an impoverished student at Birmingham University, I was brewing my own 40 pints of  barely drinkable delicious Mild Ale (pronounced ‘m + oiled’ in the local dialect).  And while I never got into the brewing habit big time, I still on occasion reach for the demijohn and yeast – like recently, prompted by the  promise of summer blackberries and the pungent whiff of Thames-side hops.

It’s obvious booze is an educational resource we ignore at our peril; but to consolidate, consider what’s going on in that murky ochre, as it sits in my hall, infusing the carpets and curtains with its fruity ambience.   I hope it’s this:

 

C12H22O11  + H2O   ->   C6H12O6 +    C6H12O6

Sucrose        Water        Glucose           Fructose

 

followed by this:

C6H12O6 ->   2C2H5OH    +    2CO2

(Glucose/Fructose)           Alcohol (Ethanol)          Carbon Dioxide

Yeast: Saccharomyces cerevisiae (Wikicommons)

The contents of the bottle are yellow because the blackberries haven’t actually appeared yet, so for now I’m using Chardonnay grape concentrate out of a can.  And as that contains fructose from the grapes plus added glucose syrup, and I’m adding sucrose on top of that, both reactions should have kicked off immediately – the whole thing enabled by one of my favourite eukaryotic micro-organisms – Saccharomyces cerevisiae: a wine yeast.

There’s nothing to do now until it ferments out, but I managed to kill 20 minutes using the chemistry and bubble rate data to figure out how things are ticking along.  I reckon I’ll produce 511g of alcohol and 488g  (273 litres) of CO2, which at the current bubble rate means the fermentation will take 6 days  (workings in the end-notes for those interested and assuming I’ve remembered my O-level chem.).

We covered production of ethanol from fermentation at school, but I don’t remember doing any distillation (which is illegal without a license in the UK).  Certainly nothing to compare with the alcohol education afforded 1960s American youth courtesy of the fabulous Golden Book of Chemistry Experiments (excerpts below), which covers fermentation with yeast plus the distillation/synthesis of ethanol, methanol, and a bunch of other fun compounds from the ethanol ‘Family Tree’:

I love the helpful precautionary note on chloroform:’THEN SNIFF CAREFULLY’.  A complete home schooling if ever there was one:

That’s all really. I’ll update with a report on the finished product, assuming the wrong types of bug and oxygen don’t intervene and vinegarate the show.

One last item though.  Yeast is of course also used in baking; the carbon dioxide from fermentation causes dough to rise.  So here’s a particularly rigorous explanation of the process from Alton Browne.   It’s over my head, but I’m sure the trained biochemists out there will relate. (Quality isn’t up to much either – sorry about that.)

 

 

References

The Golden Book of Chemistry Experiments. Robert Brent, Golden Press New York, 1960. (Anne Marie Helmenstine has a page linking to a pdf of the book at about.com)

Drink Aware http://www.drinkaware.co.uk/

Notes

Guessing there’s about 300g of glucose in the concentrate, and I know I’ve added 450g sucrose to 5.5 litres of water. As 1 Mole sucrose (242g) yields 2 Moles glucose/fructose (360g), 450g sucrose will make 669g glucose/fructose. With the 300g in the syrup that rounds up to about 1000g total C6H12O6. 1 Mole of C6H12O6 (180g) makes 2 Moles ethanol (92g) plus 2 Moles carbon dioxide (88), so 1000g should make 511g of alcohol and 488g carbon dioxide. That’s roughly half a kilo of alcohol in 5.5kg water, or, ignoring the density difference, about 10% by volume . These kits supposedly deliver 12%, so the 300g estimate was probably low. The volume of gas produced can be calculated given 1 Mole CO2 (44g) has a volume of 22.4 litres at STP (24.6 at current 25deg C room temp), so our 488g equates to 273 litres of gas having to bubble through the airlock. It’s bubbling at about 1 per second with an estimated bubble volume of half a cm3 ; so I figure at that rate it will take 6 days to ferment out. All of which seems to hang together with what it says on the tin.

ISS Pass

Three views from a pass of the International Space Station last night.

(a) From the West rising under Cancer, through Serpens on the way to Leo. (M44 Beehive cluster is just visible in Cancer if you click to enlarge)
(b) Continuing under Leo
(c) Into Virgo (heading towards Saturn on this occasion).

Taken in sequence, 22.20 GMT, 27 April 2011.   Exposure 20 seconds at f.4, ISO500, 17mm on Canon 7D.

The trail is starting to dim in the last picture, and disappeared completely over the next five seconds.

To find out when the ISS is next coming over, I get Twitter alerts from Twisst.

The Amazing Rock-eating Tree

Bit of silliness for a Sunday morning maybe.  But all the same, for those who missed it on Twitter, here is the amazing rock eating tree.

Tree growing around a piece of slate (Photo:Tim Jones)
Tree growing around a piece of slate (Photo:Tim Jones)
Tree assimilating slate
Another view (Photo:Tim Jones)

Slate-eating tree to be precise.  Tabloid hype aside, I think it’s pretty amazing to find this kind of situation undisturbed after what must be a good few years.

I took the picture last month in a disused slate quarry in North Wales, but it’s up a path that’s a wee bit off the tourist route and not so obvious.  Presumably the piece of slate either fell or was placed near the growing roots near ground level, and nature has somehow accommodated it.  The quarry was working at its peak in the late 1800’s – so who knows the real history behind this slatey vignette.

Attempts to dig out the relevant academic literature on this situation were in vane –  there isn’t any (come back if you know different).  I did find some reports on how tree roots detect and navigate around below-ground objects; but  that’s not the same.

And as this story may be old news for Twitter friends, here’s a bonus in the form of the Amazing Hat-eating Tree.

Fungus assimilating hat October 2008 (Photo:Tim Jones)
Fungus assimilating hat June 2010 (Photo:Tim Jones)
Fungus assimilating hat June 2010 (Photo:Tim Jones)

Straight-up.  I first stumbled across the beanie hat hung on a substantial piece of tree fungus back in October 2008 – caught in the clutch of  arboreal assimilation.  Then, hesitant as I am to admit to this, I made a point of revisiting the champingnoned chapeau 20 months later, still there but a little worse for wear.

All good fun, but this sort of thing does summon up those Planet of the Apes / Logan’s Run images of nature biting back following the  post-apocalyptic collapse / coalition spending cuts.  Non?

Blimey – not had so much fun since writing my definitive Ozzie the Iceman piece.