# Thread: Math topic - How does the numbers work in a lens?

1. ## Math topic - How does the numbers work in a lens?

Take the 50mm f/1.8 II as an example.

EF 50mm f/1.8 II S\$160 MM 46° 5-6 f/1.8 1.5/0.45 41 4.6/130 ES-62# 52 E-52 LP1014

Does it mean, the lights travelling in the lens form a triangle with one
side of 35mm, height of 50mm, the other two sides are equal, and the
angle opposite to this side is 46°? However,

50mm * tan(23°) * 2 <> 35mm.

What happened?

cheem....

3. ## Re: Math topic - How does the numbers work in a lens?

Originally Posted by dRebelXT
50mm * tan(23°) * 2 <> 35mm.

What happened?
The standard frame size for 35mm film is 24mm by 36mm. The diagonal of the frame is thus approximately 43mm, not 35mm.

4. ## Re: Math topic - How does the numbers work in a lens?

Originally Posted by LittleWolf
The standard frame size for 35mm film is 24mm by 36mm. The diagonal of the frame is thus approximately 43mm, not 35mm.
50mm * tan(23°) * 2 = 42.44748162mm;
(24^2 + 36^2)^0.5 = 42.43819035mm.

My numbers matched.

My question is, for this lens, the lens is 137.2mm in full length, but in full zoom it will stretch to 300mm + (137-75) = 362mm, is my numbers correct?

EF 75-300mm f/4-5.6 IS USM S\$1,200 Ultrasonic 32°11’-8°15’ 10-15 f/4-5.6 4.9/1.5 137.2 1.5 lb./670 ET-64II 58 E-58U LP1022

5. ## Re: Math topic - How does the numbers work in a lens?

Originally Posted by dRebelXT
5
My question is, for this lens, the lens is 137.2mm in full length, but in full zoom it will stretch to 300mm + (137-75) = 362mm, is my numbers correct?
The physical size of a complex lens system does not directly relate to its focal length. The principal planes (see e.g. http://hyperphysics.phy-astr.gsu.edu...t/priplan.html) may even lie completely outside of the lens. Without knowing the detailed optical design, there's little one can do to calculate it. (One can, however, find the location of the principal planes by experimental methods.)

Some zoom lenses may actually become shorter when increasing the focal length.

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