Lensmaker's equation
Today's lens manufacturing techniques have far surpassed methods used by the first lensmakers. Nowadays, the criteria for a lens is maximum power with minimal thickness. We have learned that the power of a lens is proportional to
- the index of refraction of the material used
- the radii of curvature of the lens.
The exact relationship of these factors enables an optician to know the power of a lens. This formula is known as the lensmaker's equation.
Lensmaker's equation
- f: focal length
- n: index of refraction of the lens material
- R: radius of curvature of one lens surface
- R': radius of curvature of the other lens surface
Sign convention
f:
- positive for a converging lens
- negative for a diverging lens
R:
- positive if the centre of curvature is behind the lens
- negative if the centre of curvature is in front of the lens
- infinite for a plane surface
Examples:
Refer to the diagram above and assume that the light travels from left to right, then:
Lens | R | R' |
double convex | + | - |
double concave | - | + |
