TheSkySearchers

hi all ,
what is the formula to know the percentage of increase in light capture, for say a telescope of 100 mm vs 120 mm.
I hope to make myself understood and also I hope I have chosen the right place to post.
thx .

It's a combination of focal length F and objective diameter D. The square of the focal ratio F/D (written F/<number>) is inversely proportional to the light flux on the sensor. So, an F/4 objective has a flux (7/4)^2 (about 3) times larger than an F/7 objective, and will be 3 times faster (assuming that we want to have a given number of photons on the sensor).

If you want to look at F and D separately, for a given D the light flux is inversely proportional to the square of F, and for a given F the light flux is proportional to the square of D. For a reflector you would have to correct a bit for the light blockage by the secondary mirror.

As Henk stated, the basic is just a comparison of aperture squared. So in your 120 vs 100mm frac case; it would be 120^2/100^2 or the 120 gathers 1.44 times more photons.

But, remember that one magnitude is 2.51 times more photons, so this is only a fraction of a magnitude.

Steve

You need to be more specific about what light where that you want to compare.

If you just want to compare the number of photons entering the front of the scope, that is simple: (A1 / A2) ^ 2. So, the 120mm scope will collect (120/100)^2 = 1.44 times as many photons.

If you want to compare how much light they focus per unit area at the focal plane, then you need to compare the focal ratios. Again you have to square the ratio: (Fr2 / Fr1) ^ 2. An f/4 scope will illuminate the focal plane (8/4)^2 = 4 times as brightly as an f/8 scope.

KathyNS wrote: ↑Wed Dec 28, 2022 8:06 pm You need to be more specific about what light where that you want to compare.

If you just want to compare the number of photons entering the front of the scope, that is simple: (A1 / A1) ^ 2. So, the 120mm scope will collect (120/100)^2 = 1.44 times as many photons.

If you want to compare how much light they focus per unit area at the focal plane, then you need to compare the focal ratios. Again you have to square the ratio: (Fr2 / Fr1) ^ 2. An f/4 scope will illuminate the focal plane (8/4)^2 = 4 times as brightly as an f/8 scope.

when the manufacturers say,
the 120mm picks up 40% more light than the 100mm.
how do they arrive at this calculation?

messier 111 wrote: ↑Wed Dec 28, 2022 8:48 pm

when the manufacturers say,
the 120mm picks up 40% more light than the 100mm.
how do they arrive at this calculation?

Simple approximation; the 120mm gathers 1.44 times, e.g.144%, of a 100mm. Subtract the 100% for the 4 incher and round to 40% more light.

Steve

messier 111 wrote: ↑Wed Dec 28, 2022 8:48 pm when the manufacturers say,
the 120mm picks up 40% more light than the 100mm.
how do they arrive at this calculation?

144% is 44% more than 100%. So the 120mm picks up 44% more light than the 100mm. Rounding it to 40% is reasonable for advertising copy.

messier 111 wrote: ↑Wed Dec 28, 2022 8:48 pm when the manufacturers say,
the 120mm picks up 40% more light than the 100mm.
how do they arrive at this calculation?

The area of a 100mm objective lens (50mm radius) is πx50^2 =7,854sq mm
The area of a 120mm objective lens (60mm radius) is πx60^2 =11,310 sq mm
The second area is 44% larger than the first, so it'll gather 44% more light.

thx to all of you .

As you may have noticed, area of a circle involves a pi and r^2, but when taking a ratio all that pi stuff cancels out and diameter is just as good and radius, the 2 cancels, also feet, inches, meters, mm, etc are just as good. But if you got a square scope vs a round scope then long hand is required.

Example 5 inch to 4 inch, 25/16 = 1.56, a five is slightly bigger than a 120mm.

BTW, just subtract the secondary area from the full aperture for reflectors, you'll be surprised that the secondary even up to half the primary diameter doesn't block that much light.

Steve

Just food for thought--

There is no website calculator that covers all the math discussed here above. I know because I spent all day looking for one. Now, don't get me wrong, there are calculators that cover a part of what has been discussed, but nothing that allows you to compare one OTA vs another using several ways of comparison.

I throw this out there because I'm an idea guy, not an execution guy!

JayTee wrote: ↑Thu Dec 29, 2022 11:54 pm Just food for thought--

There is no website calculator that covers all the math discussed here above. I know because I spent all day looking for one. Now, don't get me wrong, there are calculators that cover a part of what has been discussed, but nothing that allows you to compare one OTA vs another using several ways of comparison.

I throw this out there because I'm an idea guy, not an execution guy!

There are plenty of spreadsheets downloadable off the internet that will do all the scope calculations.

The calculations involved in this thread involve ratios squared. On a simple 4-function calculator, the calculations are all A ÷ B * =. Or A ÷ B ^ 2 if you have a multi-function calculator. Figuring out which scope's measurement is the numerator and which is the denominator should be intuitive.