a x b=

[Regulus (Trevor)]

Can someone give me (or point me to) the equation for determining the increase (decrease) in light gathering power between lens apertures.

Thanks - Trev

[rustigsmed (Russell)]

hi trevor

do you mean the area of the aperture? - eg pi r squared?

rusty

[Somnium (Aidan)]

piR^2 (area of a circle)

[Regulus (Trevor)]

Hi Russell.
I want to know into the future what percentage of light-gathering increase there is in going larger. Eg. How much more light gathering power does a 130mm have over a 100mm (leaving aside aperture as a consideration).

Cheers - Trev

[janoskiss (Steve H)]

Light per unit area of focal plane is determined by the f-ratio alone. Amount of light hitting a sensor there is proportional to the square of the f-ratio. For example, take f/4 vs f/6: the f/4 lens collects (6/4)-squared = 1.5 x 1.5 = 2.25 times more light per detector pixel than an f/6.

Light per unit area (or solid angle) of sky OTOH is proportional to the square of the aperture (diameter) of the lens: double the aperture gives you 4x the light; increase/decrease the aperture by factor N, you'll increase/decrease the number of photons collected from a fixed portion of the sky by factor N x N.

The reason for this perhaps counter-intuitive discrepancy between these two ways of figuring it is that if you increase the aperture but leave the f-ratio unchanged you also increase the image scale (magnification) in proportion to the aperture. So you do get more photons from a fixed bit of sky but they are spread over a larger area in the focal plane.

[Mamba (David)]

Hi Trevor,
Simply square the diameter of the objective.
eg 4 inch scope squared is 16
6 inch scope squared is 36
6 inch scope therefore collects 36 divided by 16 times more light, ie 2 1/4.
Mamba

[janoskiss (Steve H)]

Re your last post, for plain common sense visual astronomy: the 130mm will collect (130/100)-squared or 1.3 x 1.3 ~= 1.7 times more light from any given patch of sky.

[Regulus (Trevor)]

Thank you David, and Steve. Pretty much what I needed.

Cheers - Trev