Light from a distant object like a star arrives at the telescope as a bundle of parallel rays. The front lens (objective lens) captures these rays. They traverse the objective lens they are refracted (Latin to bend inward). The revised path of these rays sketches out a cone of light.

The focal length of this objective lens is taken as a measurement lens to apex of this cone when the object being viewed is a far distance, like a star said to be at distance infinity.

The image of a star being viewed forms at this apex. We can view it by allowing the cone of image forming rays to play on a white screen of ground glass (sheet of glass with roughened surface. We can also place a short focal length lens downstream of this apex and view a magnified image of the subject.

The brightness of this image is primarily due to the fact that the objective lens has a surface area that gathers light rays much like a funnel. In other words, the larger the diameter of the objective lens the more light gathered thus the brighter the objects image. Astronomers, wishing to see dim objects design telescopes with gigantic diameter.

Binoculars and terrestrial telescopes have small manageable diameter objective lenses. We are interested in how well they function in dim light. A relative brightness math formula to the rescue.

Say you are peering at night; sailors want binoculars with superior image brightness. The chosen magic numbers are 7X with a 50mm diameter objective. The 50mm (2 inch) front lens gathers the dim light. The eyepiece magnifies and objects appear 7 times closer thus 7X magnification. The light that reaches our eye come through a aperture that is 50 ÷ 7 = 7.1mm in diameter. Now the average human eye, at night has a iris opening of about 7mm (depending on age). Thus, the 7X50 binocular, or any such combination with a 7mm exit pupil passes this test.

Another formula used is Relative Brightness. What is the relative brightness of 7X50 binoculars? (50 ÷ 7)^2 = 51. How does this compare to 10X35 binoculars? Math is (35 ÷10)^2 = 12.25. Thus, the smaller binocular is 12.25 ÷ 51 = 0.24 = about 25% of brightness of a pair of 7X50 binoculars.

When light hits objects it can traverse or reflect away, it can be absorbed, any combination of these. When light is absorbed, its energy is converted to heat, if you are peering at the sun with telescope or binoculars, if precautions are not taken, the brightness of the image will be converted to hear and you likely will suffer eye damage.

Use approved filters to be safe, not sorry.

Light from a distant object like a star arrives at the telescope as a bundle of parallel rays. The front lens (objective lens) captures these rays. As they traverse the objective lens they are refracted (Latin to bend inward). The revised path of these rays sketches out a cone of light.

The focal length of this objective lens is taken as a measurement lens-to-apex of this cone when the object being viewed is a far distance; like a star said to be at distance infinity.

The image of a star being viewed forms at this apex. We can view it by allowing the cone of image forming rays to play on a white screen of ground glass (sheet of glass with roughened surface). We can also place a short focal length lens downstream of this apex and view a magnified image of the subject.

The brightness of this image is primarily due to the fact that the objective lens has a surface area that gathers light rays much like a funnel. In other words, the larger the diameter of the objective lens the more light gathered; thus the brighter the object's image. Astronomers, wishing to see dim objects design telescopes with gigantic diameter.

Binoculars and terrestrial telescopes have small manageable diameter objective lenses. We are interested in how well they function in dim light. A relative brightness math formula to the rescue.

Say you are peering at night; sailors want binoculars with superior image brightness. The chosen magic numbers are 7X with a 50mm diameter objective. The 50mm (2 inch) front lens gathers the dim light. The eyepiece magnifies and objects appear 7 times closer; thus 7X magnification. The light that reaches our eye come through a aperture that is 50 ÷ 7 = 7.1mm in diameter. Now the average human eye, at night has a iris opening of about 7mm (depending on age). Thus, the 7X50 binocular, or any such combination with a 7mm exit pupil, passes this test.

Another formula used is Relative Brightness. What is the relative brightness of 7X50 binoculars? (50 ÷ 7)^2 = 51. How does this compare to 10X35 binoculars? Math is (35 ÷10)^2 = 12.25. Thus, the smaller binocular is 12.25 ÷ 51 = 0.24 = about 25% of brightness of a pair of 7X50 binoculars.

When light hits objects it can traverse or reflect away or it can be absorbed -- any combination of these. When light is absorbed, its energy is converted to heat. If you are peering at the sun with telescope or binoculars, if precautions are not taken, the brightness of the image will be converted to heat and you likely will suffer eye damage.

Use approved filters to be safe, not sorry.