Summary of Mirrors and Lenses

We reiterate some of the important points made in this section of our work. Our results are valid for spherical mirrors and lenses, for sources close to the optical axis.

Sign Conventions

Let Side A of an optical component be the side from which light starts, and let Side B be the side to which light travels. With mirrors, Sides A and B are identical. If s is the source distance, i is the image distance, R is the radius of curvature, and f is the focal length, then, our sign conventions are as follows.

Image Position

For mirrors, the source distance s, image distance i, and focal length f satisfy the equation

1/s + 1/i = 1/f

For lenses, they satisfy the equation

Image position for lenses.

where n1 is the index of refraction for the region surrounding the lens, and n2 is the index for the lens itself. R1 and R2 are the radii of curvature for the first and second surfaces of the lens respectively. In air, this equation reduces to the lens-makers' equation,

The lens-makers' equation.

where n is the index of the lens.


The focal length of a mirror is very nearly half of its radius,

f = R/2

For a thin lens, the focal length is found using the image-source equation, taking s to approach infinity. In air, the symmetric foci of a lens are f units away from the lens, where f satisfies

Focus of a lens in air.


The magnification of a mirror or a lens is the ratio of the image distance to the source distance,

M = -i/s

M is negative if the image is upside down, and positive if it is right side up.

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