**Focal Length Calculator**

Focal Length |
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Refractive Index_{lens} |
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Refractive Index_{medium} |
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Radius_{1} |
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Radius_{2} |
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## Definition

**Focal length** is defined as the distance from the surface of a lens or mirror to the point where the light rays converge to form an image(the point of focus).

Focal length of lens is usually measured in millimetres (mm). In the case of zoom lenses, both the minimum and maximum focal lengths are stated, for example 15–52 mm

Focal length of a convex lens is represented with positive(+) sign while focal length of concave lens is represented with negative(-).

## Formula

The principal focal length of a lens is determined by the index of refraction of the glass, the radii of curvature of the surfaces, and the medium in which the lens resides. It can be calculated from the lens-maker’s formula

1/f = ((nl / nm) – 1) {(1/R_{1}) – (1/R_{2})}

**Where:**

f |
Focal length |

nl |
Refractive index of lens |

nm |
Refractive index of medium |

R_{1} and R_{2} |
Radii of curvature of the two surfaces of the lens |

Focal length (f) of combination of two thin lenses in contact:

1/f = (1/f_{1}) + (1/f_{2})

Where, f1 and f2 are focal length of respective lenses

**For Example:**

The radius of curvature of a lens is 100 cm at the front and -200 cm at the back. Refractive index of the material is 1.37. The values of the key variables are:

R_{1} |
= | 100 cm |

R_{2} |
= | 200 cm |

nl | = | 1.37 |

nm | = | 1 |

**Sol. :**

1/f = ((1.37/1) – 1) {(1/100) – (1/200)}

**Focal Length = 1.8 m**

## Units

SI unit of focal length is meter(m).