Tag Archives: newton

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

Unweaving the Rainbow

I took this short sequence in the garden this afternoon.  No photo-shopping, just a nice illustration of the splitting of sunlight into it’s component colors by refraction through a water drop – shuddering in the breeze after a storm.

rainbowThe simplest of things, it put me in mind of John Keats’s supposed lament that Isaac Newton had destroyed the beauty of the rainbow by explaining the science behind it, the underlying sentiment of which he included in the poem Lamia.  I say supposed, because I can’t find a primary reference to Keats actually ‘having a go’ at Newton over his prism or whatever.  Lamia however speaks for itself (see below).

Rainbow over LondonRichard Dawkins gives an alternative view in his book, Unweaving the Rainbow, where he argues scientific understanding enhances rather than diminishes beauty.  I’m with Dawkins on this one.  And while those going through life without a scientific education (for whatever reason) experience it in a way that is different, I believe they are also simply missing out.

Keats’s rainbow reference appears in his poem Lamia Part II:

What wreath for Lamia? What for Lycius?
What for the sage, old Apollonius?
Upon her aching forehead be there hung
The leaves of willow and of adder’s tongue;
And for the youth, quick, let us strip for him
The thyrsus, that his watching eyes may swim
Into forgetfulness; and, for the sage,
Let spear-grass and the spiteful thistle wage
War on his temples. Do not all charms fly At the mere touch of cold philosophy?
There was an awful rainbow once in heaven:
We know her woof, her texture; she is given
In the dull catalogue of common things.
Philosophy will clip an Angel’s wings,
Conquer all mysteries by rule and line,
Empty the haunted air, and gnomed mine—
Unweave a rainbow, as it erewhile made
The tender-person’d Lamia melt into a shade.