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Radiometry and photometry in astronomy

Long answer (let's pretend we have a conversation with someone who believes viewing the full moon through the 5-meter Hale telescope will damage the eye):

Q: The Hale telescope will gather 500,000 times more light than the 7 mm pupil of the naked eye. The Sun is 500,000 times brighter than the Full Moon. Doesn't that mean that a view of the Full Moon through the Hale telescope would look as bright as the Sun and therefore could damage your eye, as viewing the Sun naked-eye can do?

A: No. If you view the Moon through the Hale telescope, using a magnification of 100x, then the exit pupil will be 50 mm, which means that most of the lunar light will be blocked by the 7 mm pupil of your eye. You'll really be using only some 0.7 meters of the 5-meter aperture of the Hale telescope at 100x magnification.

Q: OK, then let's increase the magnification to 700x, in order to bring down the exit pupil to 7 mm such that all the light can enter the eye's pupil. Won't that damage the eye?

A: No. The apparent size of the naked-eye Moon is 1/2 degree. If you magnify this 700x, the apparent diameter of the magnified Moon should be some 350 degrees! No eyepiece will have such a large apparent field of view, and even the eye itself is able to see a field of view only some 180 degrees large. The largest field of view in eyepieces is some 120 degrees, which means that, at the very most, only about 1/10 of the light of the Full Moon would ever reach your eye, if viewed at 700x magnification through the Hale telescope.

Q: OK, but 1/10 of the brightness of the Sun is still pretty bright. Doesn't that impose a risk of damaging the eye?

A: No, since the entire field of view will be filled with this light, while a naked-eye view of the Sun will see all the solar light concentrated in a small circle only some 1/2 degrees across. In fact, viewing the Full Moon though the Hale telescope or through any large telescope, at any magnification, would be no brighter than a naked-eye view of a bright overcast sky in daytime - and that won't damage your eyes, will it?

17. Does a big telescope suffer more from light pollution than a small telescope?

By Tom Polakis

Short answer: No!!!!

Long answer: The simple-minded claim is that under conditions of bad light pollution, beyond some certain aperture, you gain very little or nothing over a smaller telescope. The claim also is that this crossover aperture becomes smaller under progressively worse conditions of light pollution.

The physics is pretty simple: "aperture always wins". It is a simple matter of signal-to-noise: in any scene a telescope does not magically brighten the sky background while not brightening the celestial target at the same time. Yet the claim being made by most folks is that the background is indeed enhanced.

Take this notion to an extreme of really bad light pollution: daytime! If the expections of this urban legend hold, then "theoretically" the naked eye should show things in the sky better than any telescope. But you can see no stars with the naked eye in daylight (let's talk noontime here, not 10 minutes before sunset), whereas you can see stars in even small a telescope without much difficulty. (Try it! First a bright star like Vega. Figure out how to get to it with your telescope, and go look at it some clear day at 11 in the morning. Is Vega easier to see in a 6x30mm finder or a 16-inch? Now go for Altair, then Deneb...and how much fainter?)

If you wish to learn a lot more about this subject -- which will help you become a better observer -- go to Mel Bartels' Web site http://www.efn.org/~mbartels/aa/visual.html and read the stuff by him and by Nils Olof Carlin about visual detection thresholds. Apply the equations there to dark, light-polluted, and daytime sky brightness values to see what happens, and to prove to yourself that this light-pollution/aperture claim is pure baloney.

A. References: Books

B. References: Web sites