In article ,
Anthony E Anson wrote:
The message
from (Nick Maclaren) contains these words:

As I said, that isn't the point. What matters is the proportion of
the NEAR-NORMAL light that is transmitted, and that is going to be
above 50%, perhaps 80%. It drops off to zero at the periphery, but
that is irrelevant.

But it isn't - I'd be surprised if 15% of incident light exited
directly. Without a lot of calculations and data which I haven't got to
hand - and may not have at all now, I couldn't work out a figure.

I would be EXTREMELY surprised if the proportion of near-normal light
that is transmitted is less than 50%.

Then, in the very unlikely event of any part of the leaf touching the
focus, your whole hypothesis falls over because the sun continues to
move the goalposts.

Which is why the sun focussed through discarded bottles never causes
fires, I suppose. You do know that it does, don't you?

The refractive index of glass and water are entirely different, as are
the shapes of (say) the broken bottom of a bottle and a globe.

Eh? 1.5 versus 1.33. Not that different.

The point is that (say) all of the radiation passing through a circle
of radius 0.1 mm is concentrated into a circle of (say) 0.01 mm,
multiplied by the transmittance (say 0.5). This is 50 times as strong
as the incident sun, and is quite capable of doing cell damage in
seconds.

But your arithmetic is wrong: we are talking about spheres, not circles.
If the light incident on a globe of radius ·1mm is concentrated in to a
circle of radius ·01mm you have to take the amount of light which passes
through, which is way less than 50%. The greatest loss is caused by the
inability of light to escape from water to air if the angle of incidence
is over a certain figure, and this is a lot less than yhe other way
round.

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.

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

Yes.

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.

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.

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.


Regards,
Nick Maclaren.