Lens maker’s formula is used by the lens manufacturers, for manufacturing of the lenses having the desired focal length. For different optical instruments, lenses having different focal lengths are used. The focal length of the lens is dependent on the radii of curvature and the refractive index of the lens. The lens maker’s equation is another formula and it gives the relationship between the radii of curvature, refractive index, focal length, of the two spheres that are used in the lenses. The lens maker’s formula can be described as below.
Here f represents the focal length, n is the refractive index of the material that is used to make the lens, R1 is the radius of the curvature of the first sphere, and R2 is the radius of curvature of sphere 2. But this equation can only be used for the thin lenses. The lenses, whose thickness is too less to be considered as negligible, as compared to the radius of curvature can be referred to as thin lenses.
For the thin lenses, the power of the lens is approximately the sum of the surface powers. The radii of curvature can be measured according to the cartesian sign convention. The radius is positive for the double convex lenses, and its measurement is done on the front surfaces. R2 radius is negative, as it is extending to the left side from the surface of the second one. Sometimes, it may happen that the thickness of the lens is ignored, but sometimes, it is considered. The trouble of this concept can be resolved by the statement that when the ray of light is traveling from the medium or air to the medium of the lens, then it is undergoing the refraction. It is possible to ignore the double refraction if the optic’s lenses are thin enough for making the assumption that the light is refracted for only 1 time. This can be done, by making the ray optical calculation simpler, but at the first step, the constituents of thick and thin lenses should be identified.
Assumptions for Derivation of Lens Maker’s Formula
- The lens is thin and its distance measured from poles of surfaces can be considered as equal to the distance, from the optical center of the lens.
- Only the point objects are considered.
- The aperture of the lens is small.
- The refracted and incident rays make the small angles.
Limitations of Lens Maker’s Formula
The medium on both sides of lenses should be the same. The lenses should be thin. Due to this reason, the separation between two of the refracting surfaces will also be small.
