Image through a telescope can never be brighter than the image with the unaided eye

[gazza63]

Evening everyone

Seeing as it is full of cloud.....AGAIN !

I roamed the WEB, and found this to be interesting.

Hope you like, and understand it.

How much more light a telescope gathers compared to the unaided eye is determined by the ratio between the light-gathering area of the telescope and the light-gathering area of the eye. The aperture of the eye is determined by the size of the pupil (see the section below on The Human Eye for more details). In general, the average pupil will open up to about 7mm in diameter. Note that this means if the beam of light coming out of the telescope eyepiece is larger than the maximum size of the eye, the eye becomes the limiting factor and effectively reduces the aperture of the telescope. This is described more later. The light gathering area of the 7mm pupil is then 0.06 in². For the 8" telescope, this gives a ratio of 50/0.06 = 833, meaning an 8" telescope gathers 833 times more light than the unaided eye.

Above: The difference in relative size between an 8" (200mm) mirror and the 7mm opening of the human eye

This implies an object seen with the unaided eye will appear more than 800 times brighter through an 8" telescope. However, the situation is more complicated than that. While the previous statement is true for point sources (stars) it is not true for extended objects (galaxies, nebulae, planets). This is because the light from an extended object is being spread out by the fact that the telescope is magnifying the image. So magnification factors into the equation; light is lost in proportion to the square of the magnification. There is a minimum magnification allowed by the limiting size of the pupil as described above. This works out such that the image through a telescope can never be brighter than the image as seen with the unaided eye. This seems counterintuitive. However, with optimum magnification (described below) the image not be significantly dimmer and will be considerably larger and more detailed.

An additional advantage of aperture that comes into play when magnification is considered is image brightness at a given magnification. Through a given telescope, doubling the magnification reduces the brightness of an extended object fourfold. Doubling the aperture of a telescope makes the image four times brighter at the same magnification, or allows twice the magnification to be used while retaining the same image brightness.

The direct ratio between telescope brightness and unaided eye brightness still holds for point sources. For this reason, stars will appear brighter than they do with the eye, independent of magnification. The magnitude scale used to describe the brightness of stars is a logarithmic scale. Each magnitude is a difference of 2.5 in brightness. A 1st magnitude star is 2.5 times brighter than a 2nd magnitude star. A 2nd magnitude star is 2.5 times brighter than a 3rd magnitude star. And the difference between a 1st magnitude star and 3rd magnitude star is 2.5 x 2.5 = 6.25 times. A telescope which can make stars appear 833 times brighter than the unaided eye will allow stars 7.3 magnitudes fainter to be seen. If you can see 6th magnitude stars with the unaided eye, you should be able to see 13th magnitude stars through an 8" telescope. In actuality, fainter stars can be seen. This is because of the decrease in brightness of the sky background seen through the telescope. Sky brightness is also a function of magnification, the sky growing darker as the power is increased. At a magnification of 100x, the sky background appears 2.7 magnitudes darker than without the telescope, which translates to an extra 2 magnitudes of reach, allowing 15th magnitude stars to be seen. A darker sky which allows fainter stars to be seen with the unaided eye will of course allow even fainter stars to be seen through the telescope.

[Moonshane]

Indeed Gary, this is why you can never hurt your eye looking at the moon through a scope. some people find it uncomfortable but this is more likely to be a factor of their eye not the light I suspect.

[Pig]

very interesting but I am not sure about the title of the main thread

If you cannot see a star with the naked eye there is no measurement to be had (I am not disputing that a star is there)

If you can see it with the scope it must be brighter regardless of the magnification

However if you mean from 1 - 6ish magnitude I can grasp that

[gazza63]

very interesting but I am not sure about the title of the main thread

If you cannot see a star with the naked eye there is no measurement to be had (I am not disputing that a star is there)

If you can see it with the scope it must be brighter regardless of the magnification

However if you mean from 1 - 6ish magnitude I can grasp that

That's exactly my thought? I guess, it's going by what the scope and unaided eye can see (brightness wise).

[gazza63]

If we had eyes like this Tarzier......Think of the possibilities?

[LukeSkywatcher]

If we had eyes like this Tarzier......Think of the possibilities?

If only some of us were as cute as him too.