Mirrors & Monkey Tricks

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Ishani is now into her eighth month. She is no longer amused by spinning tops and gyroscopes...thinks they are the idle playthings of nitwit boys.

The only way to focus her when she is distracted and restless is to stand her in front of her Dressing Table Mirror. She is then enchanted and transfixed...which will last a lifetime {;-)

I guess mirrors are as ancient as women. As long ago as Cleopatra's regime, huge concave mirrors were regularly used to track enemy ships and burn them by focusing sunlight on the poor blighters.

Mirror-making is an art as well as a craft. Huge mirrors for big telescopes like the Mt Wilson and the Hubble are a challenge to make to required perfection (in Physics there is nothing called 'Perfection'; only to within (+) or (-) some number).

Unending are the antics of monkeys with mirrors. At least one problem was there in the early Editions of Resnick & Halliday where you are to show that a monkey clinging to one end of a rope on a pulley can never get rid of her image in the balancing mirror hanging from the other end, however hard she climbs up or down.

Mahabharat was fought largely because Draupadi snickered at Duryodhan when he was inveigled into entering what he thought was a pool of water, an illusion created in the Hall of Mirrors in Mayasabha. Women!

My friend NP, his wife and two sons returned from a pilgrimage to the famous Hill Temple at Srisailam. That day they were having their lunch with us at our place in KGP. All four of them were excited about its Hall of Mirrors. In particular, they were led to a nook by an old resident woman. She asked them to look at their own reflections at a corner between the wall-mirror and the ceiling-mirror. And asked what they saw. Each of them replied that they could see their own reflected image perfectly but it was BLIND! Whereupon the old woman said only folks who have never sinned in thought, word or deed could escape their own blind image (And of course they parted with some hard cash to expiate their sins).

I told them it must be a trick of ray optics, nothing more; but they were not convinced. So I had to take a day off and draw a set of ray-diagrams, which led to many more interesting results, like images with multiple sets of eyes (happy!) and noses (not so happy). They were convinced only when I took them to our wash-basin-mirror and asked them to hold up another mirror over their heads horizontally touching the wash-basin-mirror and tilting it at various angles slowly from an acute through a right angle (Srisailam thing) to obtuse angles continuously. They were just amazed and I had to publish an Article with him in Physics Education of Poona as a Problem with its Solution in the next issue. Anupam Mazumdar (as expected) at once did it for himself at the wash-basin-mirror in his Hall. But very unexpectedly, so did our ex-Director Professor G S Sanyal (May His Tribe Increase!).

When I was a student I wanted a clear explanation of the fact that when a beam of light falls on a slab of glass, the refracted ray has the same frequency but a different wavelength (speed of light in glass being less). I asked many why it is not the other way round, meaning that wavelength could remain the same and frequency decrease. As usual I was snubbed for asking such a trivial question ("Everybody knows..."). And I had to find my answer myself to my own satisfaction decades later.

It can be explained in two equivalent ways:

(1) Mathematical: We derive the Fresnel relations for the reflection and transmission coefficients using boundary conditions. Note that the frequency has to remain the same just because the boundary is at one plane in space (x=0) for all times. [Try the other way round and amuse yourself why space and time are on a different footing though Taylor and Wheeler dub it 'spacetime' (one word, my foot!)].

(2) Physical: The incoming electromagnetic wave sets up the bound electrons in glass into forced oscillations, and these then re-radiate giving the reflected and transmitted light waves (Extinction Theorem). And everybody knows that, in the steady state, forced oscillations have the same frequency as the forcing oscillations and so is the frequency of re-radiated waves.

Both these are modified when the glass slab starts moving, say (1) parallel to its surface and (2) perpendicular to its surface. In these situations both frequency and the wavelengths change in general. These can again be deduced by the two methods given above: In one explanation, the boundary condition is at a moving boundary; while in the other, it is just the well-known Doppler Effect.

This explains why inter-stellar microwave photons bouncing off relativistic protons of cosmic rays return escalated in frequency as Gamma-ray photons. My students in the IV Year Lab used to simulate this Movie using the 'Relativistic Collision' Program of Edwin Taylor's Spacetime Software. Everything about light is ultra-relativistic; light moving always with the pristine invariant speed c!

RSS was very much interested in this and we published it in Physics Education (Great Britain).

[Last Laugh: Bertie Wooster was always amazed at the discreet and silent way in which Jeeves materializes into his room carrying the breakfast tray; which he compares to the trick of Indian Yogis who disappear in Bombay and reassemble themselves in Calcutta.

Bertie then hazards his opinion that they must be doing it with mirrors!]

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