How TeleConverters Affect
Magnification

Prepared 2007-02-28 (169/12917) by Bill Claff

TeleConverters (TCs) operate by
the same lens combination principles as close-up lenses.

The basic formulas are:

P = P_{1} + P_{2} - d_{m} * P_{1} * P_{2}

Where

P, P_{1}, and P_{1} are lens powers in diopters

d_{m} is the distance between lens nodes of P_{1} and P_{2}
in meters

And

H_{11}H_{1} = d_{m} * P_{2} / P

H_{22}H_{2} = -d_{m} * P_{1} / P

For the distance the resulting lens nodes shift as a result of a non-zero d_{m}

For close-up lenses we often disregard d_{m} which simplies
calculations considerably.

(See How
Close-up Lenses Affect Magnification)

However, the design of a TC is more complex since in addition to changing focal
length the rear node must also move to maintain infinity focus.

Because of the placement and movement of the rear node, the term d_{m}
in the power equations cannot be disregarded.

So without complete lens and TC information, only the effect on focal length at
infinity focus and the effect on magnification at any focus position can be
easily calculated.

In a suprising twist, the effect of the TC multiplier decreases as the
magnification of the primary lens increases and can go below 1 resulting in a
decrease of focal length as you focus closer.

For example, the 105mm f/2.8G ED-IF AF-S VR Micro-Nikkor has infinity and
closest focus focal lengths of 105.2mm and 75.1mm.

With the addition of a Kenko 1.4xTC the infinity focal length increases a
factor of 1.4 from 105.2mm to 148.8mm but the closest focus focal length drops
from 75.1mm to 52.9mm.

All of the above values are actual measurements with the exception of the
148.8mm value which has been computed.

Although focal length may not be as expected at closest focus, magnification is
increased as expected; and a TC can be a suprisingly good way to get more
magnification for close-ups.