section_path: Construction of simple lenses/Lensmaker's equation
section_name: Lensmaker's equation
paragraph_text: Lensmaker's equation
  
  The (effective) focal length f {\displaystyle f} of a spherical lens in air or vacuum for paraxial rays can be calculated from the lensmaker's equation:
  
  1 f = (n − 1) , {\displaystyle {\frac {1}{\ f\ }}=(n-1)\left\,} where
  
  The focal length f is with respect to the principal planes of the lens, and the locations of the planes h 1 {\textstyle h_{1}} and h 2 {\textstyle h_{2}} with respect to the respective lens vertices are given by the following formulas, where it is a positive value if it is right to the respective vertex.
  
  h 1 = − f (n − 1) d R 2 n {\displaystyle h_{1}=-{\frac {f(n-1)d}{R_{2}n}}} h 2 = − f (n − 1) d R 1 n {\displaystyle h_{2}=-{\frac {f(n-1)d}{R_{1}n}}}
  
  f is positive for converging lenses, and negative for diverging lenses. The reciprocal of the focal length, f, is the optical power of the lens. If the focal length is in metres, this gives the optical power in dioptres (inverse metres).
  
  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. Other properties of the lens, such as the aberrations are not the same in both directions.