In optics, a thin lens is a lens with a thickness (distance along the optical axis between the two surfaces of the lens) that is negligible compared to the focal length of the lens. Lenses whose thickness is not negligible are sometimes called thick lenses.
The thin lens approximation ignores optical effects due to the thickness of lenses and simplifies ray tracing calculations. It is often combined with the paraxial approximation in techniques such as ray transfer matrix analysis.
The focal length, f, of a thin lens is given by a simplification of the Lensmaker's equation:
where n is the index of refraction of the lens material, and R1 and R2 are the radii of curvature of the two surfaces. Here, R1 is taken to be positive if the first surface is convex, and negative if the surface is concave. The signs are reversed for the back surface of the lens: R2 is positive if the surface is concave, and negative if it is convex. This is an arbitrary sign convention; some authors choose different signs for the radii, which changes the equation for the focal length. For thicker lenses the full version of the Lensmakers equation is required, containing an additional term relating to the thickness of the lens.
Certain rays follow simple rules when passing through a thin lens, in the paraxial ray approximation:
- Any ray that enters parallel to the axis on one side of the lens proceeds towards the focal point F on the other side.
- Any ray that arrives at the lens after passing through the focal point on the front side, comes out parallel to the axis on the other side.
- Any ray that passes through the center of the lens will not change its direction.
By tracing these rays, the relationship between the object distance s and the image distance s' can be shown to be
In scalar wave optics a lens is a part which shifts the phase of the wave-front. Mathematically this can be understood as a multiplication of the wave-front with the following function: