Question

Why does a lens have two radii?​

Answer 1

Answer:

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A lens is a little more complicated than a mirror.

A mirror behaves mathematically as if the index were -1 and it only has one relevant surface.

A lens has two surfaces, distance between them, and a refractive index, and all of those properties affect the focal length.

The formula for the focal length of a lens in a vacuum is given by:

[math] \frac{1}{f} = ( n − 1 ) [\frac{1}{R_1} − \frac{1}{R_2}+\frac{( n − 1 )d}{n R_1 R_2}][/math]

where

f is the focal length

[math]R_1[/math] is the radius of curvature of the first surface

[math]R_2[/math] is the radius of curvature of the second surface

n is the index of refraction of the lens

d is the distance between the two surfaces

Note that this formula is only for rays that are very close to collimated and near the center of the lens.

Obviously if you change any of the parameters, not just one radius, you get a change in the focal length of the lens.

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