Thin lens

A lens can be considered a thin lens if d << f.

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 the Lensmaker's equation:

$\frac{1}{f} \approx \left(n-1\right)\left[ \frac{1}{R_1} - \frac{1}{R_2} \right],$

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 a thin lens, in the paraxial ray approximation, the object (s) and image (s') distances are related by the equation

${1\over s} + {1\over s'} = {1\over f}$.

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:^{[citation needed]}

$\exp\left(\frac{2\pi i}{\lambda} \frac{r^2}{2f}\right)$.