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Lensmaker’s equation

The focal length of a lens in air can be calculated from the lensmaker’s equation:
1/f = (n – 1)(1/(R_1) – 1/(R_2) + ((n – 1)d)/(n(R_1)(R_2))), where

f is the focal length of the lens,
n is the refractive index of the lens material,
R_1 is the radius of curvature of the lens surface closest to the light source,
R_2 is the radius of curvature of the lens surface farthest from the light source, and
d is the thickness of the lens (the distance along the lens axis between the two surface vertices).

Sign convention of lens radii R_1 and R_2

The signs of the lens’radii of curvature indicate whether the corresponding surfaces are convex or concave. The sign convention used to represent this varies, but in this article if R_1 is positive the first surface is convex, and if R_1 is negative the surface is concave. The signs are reversed for the back surface of the lens: if R_2 is positive the surface is concave, and if R_2 is negative the surface is convex. If either radius is infinite, the corresponding surface is flat.

Thin lens equation

If d is small compared to R_1 and R_2, then the thin lens approximation can be made. For a lens in air, f is then given by
1/f ≈ (n – 1)(1/(R_1) – 1/(R_2))

The focal length f is positive for converging lenses, negative for diverging lenses, and infinite for meniscus lenses. The value 1/f is known as the optical power of the lens, and so meniscus lenses are said to have zero power. Lens power is measured in dioptres, which are units equal to inverse meters (m^(– 1)).
Lenses have the same focal length when light travels from the back to the front as when light goes from the front to the back, although other properties of the lens, such as the aberrations are not necessarily the same in both directions.

lens equation:
1/u + 1/v = 1/f

where u is the distance from object to lens
v is the distance from image to lens
f is the focal length