How Extension Tubes Affect
Magnification

Prepared 2007-02-02 (169/12612) by Bill Claff

The following formula governs
the mathematics of achieving closer focusing and increased magnification by using
extension tubes or close-up lenses.

v = ( 1 + m ) * f

Where:

v is the distance from the rear principal plane of the lens to the focal plane

m is magnification

f is focal length

Note that it is common for the focal length of a lens to decrease as you focus
closer than infinity.

See Estimating Focal Length at Closest Focus
for details on estimating the closest focus focal length.

Using the result of the above referenced post for the 300mm f/4D ED-IF AF-S
Nikkor we have the following values:

focus |
f |
v |
m |

infinity |
300mm |
300mm |
0 |

closest |
242.9mm |
308.5mm |
.27 |

Note that in addition to reducing focal length there is a slight internal
extension of this lens during focusing.

We can rearrange the formula for v to solve for m

m = v / f - 1

It's clear from this formula that if we increase v by x them m increases by x /
f, ie.

m_{x} = ( v + x ) / f - 1 = m + x / f

So, if we add 68mm of tubes to the above example

focus |
x / f |
m |
S |

infinity |
.23 (68/300) |
.23 (0 + .23) |
1973mm |

closest |
.28 (68/242.9) |
.55 (.27 + .28) |
1061mm |