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Re: [ATM] Extended Object Brightness
On a more serious note that my last post (which was focused more on the
humour of the situation).... This is similar (if not the same) to the
discussion about two years ago; where we had a thought experiment regarding
lunar observing. The question was whether it was possible for a telescope
of sufficient aperture, pointed at the moon, to cause eye damage.
The key to explaining why it would not cause such damage was the "surface
brightness" limitations of an optical system. If I understand this
correctly (and please point out any error in my thinking... this discussion
drives me crazy) a telescope returning collimated light can never deliver
energy beyond the surface brightness (stellar magnitude per unit area) of
the object being observed. Related to this, I presume two things.... and
this is where I stay up all night losing my mind over useless thought
experiments....
1. The maximum energy delivered by any optical system can never exceed the
surface brightness of the source. Since you can lay down on the moon during
the day without incinerating your space-suit, you can never do damage to
your eye, no matter how big your aperture or how close you are to the
object.
2. Viewing individual stars with large aperture scopes does not cause
damage to the eye because of the diffraction limited nature of telescope
optics. Under high enough magnification, the airy disk diffuses the light,
actually lowering the apparent brightness. That's why we don't burn tiny
little holes in our eyeballs when looking at distant stars (even if they are
really hot!).
The sun, being an extremely hot and diffuse object (defining diffuse as
something taking up measurable arc-seconds in the sky) can be delivered to
the observer at a total energy level proportional to magnification. This
total energy and its wavelength is mathematically related (in some fashion)
to the surface brightness of the object. As aperture increases, more energy
is delivered in the area of the eyepiece's exit pupil, with the total energy
never exceeding an "aperture sized" piece of the object itself (less the
effect of atmospheric and optical diffraction, which is considerable).
Nonetheless, a 10" piece of the sun would be a mighty uncomfortable thing.
So, I'm not sure about Ken's post below... A nebula is no different from the
sun from an optical perspective. I maintain that in both cases, the energy
will never exceed the surface brightness. Although nebulae contain hot gas,
they have very low surface brightness because the gas is highly dispersed.
If there was a full blown star (set aside the Chandrasekher limit for a
moment) taking up the entire space occupied by the Orion nebula at the same
distance, you'd blow out your eye looking at it with a telescope.
Another example I was contemplating last night was this absurd scenario....
Imagine you are in deep space, between galaxies. You purchase (from the
Romulan empire) a billion perfectly shaped cubes of ice, each 10,000 miles
in length, width and height. You build a wall out of this ice, facing a
large telescope located a light year or so away. Ok, the telescope is
infrared... This wall of ice is an extremely hot object relative to the
surrounding space; a huge amount of energy is eminating from it. No matter
how large an aperture we build, no-one is going to suffer eye damage looking
at it. The surface brightness is still zero degrees centigrade.
Now, a more interesting question is whether or not a telescope of
sufficiently large aperture can function as a refrigerator!
Thanks for putting up w/ my ramblings...
RO
----- Original Message -----
From: "Ken Hunter" <atm_ken_hunter@yahoo.com>
To: <richas@earthlink.net>
Cc: <atm@atmlist.net>
Sent: Sunday, April 11, 2004 7:52 AM
Subject: Re: [ATM] Extended Object Brightness
--- Richard Schwartz <richas@earthlink.net> wrote:
> OK, point the telescope at the sun, put a
> hundred-dollar bill behind the
> eyepiece, and observe. Is that what you want to
> have happen to your
> eyeball?
>
>
NO! What he's asking is if the telescope can collect
and concentrate energy of an extended object. Yes for
the Sun and No for the Nebula... That's what he's
being told and he's just asking why.
Ken Hunter
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