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14-05-2003, 09:56 AM

The message
from (Nick Maclaren) contains these words:

\snip\
Sigh. I am talking about a sphere of (say) 1 mm diameter. The light
that passes within 6 degrees of normality will enter within a circle
of 0.1 mm diameter. Elementary geometry. I do NOT believe your
claim that most such near-normal light is reflected - if it were,
you couldn't look down at the bottom of a shallow pool with the sun
overhead.

Please keep up at the back there. Light incident on a flat surface will
all enter up to a much wider angle than light exiting.

A globe has not got a flat surface, and the angle of incidence of light
falling on that surface is modified rapidly the futher from the axis of
incidence on the sphere.

But the main filter is when the light which *DOES* get through meets the
(effectively) concave mirror of the bottom of the droplet.

Have you ever looked at the surface of a swimming pool from under water?

Yes.

And what did you see beyond it? If you remember seeing very much it
would be the triumph of imagination over memory.

At that distance (say a 1 mm radius droplet), the rotation of the
earth means that the focus will move 0.01 mm in 45 seconds, so it
will burn a path through the cells.

And it doesn't. Look at any leaf you like after the sun has been sining
following a light shower.

The chances of the focus being close to the leaf are low. As I said,
I have seen the focussing effect with water droplets, though I have
not seen it happen precisely enough to cause tissue damage. That
does not mean that it doesn't happen.

Well, I hold that it does. As do the experts on Gardeners' Question Time.

And, just to complete the argument, all of the rays that I am
considering hit the droplet within 3 degrees of normal, and so the
reflection is definitely small and the focussing is good.

They can't. It is in the nature of droplets to have a surface which is
curved in two planes.

Ye gods and little fishes!

If you shine a parallel beam at a sphere, the rays that hit within
N degrees of normal define a circle on the surface of the sphere. All
of lens theory is based around the theory of near-normal rays - well,
at A-level, it is - it gets a bit more complex later on.

Ye Gods and bigger fishes! Any parallel light striking a sphere will
illuminate totally an area of a median cross-section of that sphere.
What is this red-herring of 'N degrees?

However, the actual curvature of the surface drops away as a function of
pi and the diameter, rapidly increasing the angle of incidence of light
falling on it.

But I can't see our differences being resolved without the application
of Very Hard Sums.

I haven't seen the damage in real life, but that is largely because
the conditions for it to occur are rare in the UK. I do believe
that it happens, though I agree that it isn't the major danger that
many books make it out to be.

another sigh
I would have thought that the conditions in the British Isles would have
been ideal for the trials.
/sigh

Clearly. But that is because you haven't looked deeply enough into
the issue. It is extremely rare that the sort of showers that form
many droplets on leaves are followed by strong sun - it is far more
common for the resulting sun to be weak or even watery. This is
not true in the tropics.

Remember that even direct sun at midsummer in the UK is rarely more
than 50% of the earth's insolation, and it is common for it to drop
to 10% or less even on bright days. Yes, we really DO get that
little sunlight here, largely because of the amount and wetness of
the atmosphere that the light has to travel through.

Ah, but perhaps I have the advantage here, having lived in the North
West of Scotland, and where my occupatin has taken me to altitudes of
over 3,000 feet, where minute droplets of water are rather more common
than is desirable for personal comfort.

BTW, if any battle fails to be joined on what you may hope is a
contentious issue, don't think that I've parked my armour under the bed
and stabled the destrier: our ISP has recently 'improved' the newsfeed
and a few posts are evaporating in the midday sun.

Either I may not see your nonsense or you might not see my wonderfully
reasoned arguments ;-p

(Ask Janet & John, Helen Vecht or Anne Jackson)

--
Tony
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