Question

What is the relation between focal length and radius of a lens?

Answer 1

Answer on Question #73750, Physics / Optics

Question. What is the relation between focal length and radius of a lens?

Answer.

First, if we have in mind the radius of curvature, then the relation between focal length and radius of curvature of a lens

$$f = - \frac {n _ {0}}{\Phi}; f ^ {\prime} = \frac {n _ {2}}{\Phi},$$

where

$$\Phi = \frac {n _ {1} [ (n _ {2} - n _ {1}) R _ {1} + (n _ {1} - n _ {0}) R _ {2} ] - (n _ {1} - n _ {0}) (n _ {2} - n _ {1}) d}{n _ {1} R _ {1} R _ {2}};$$

$n_0, n_1, n_2$ - refractive indexes; $R_1, R_2$ - radii of curvature; $d$ - the thickness of the lens.

Second, if we mean the radius of the lens itself, then the focal length does not depend on it. Lens speed depends on the radius of the lens.

(More detail see Max Born & Emil Wolf Principles of Optics)

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