Calculating effective aperture with teleconverter

[ray_parkhurst]

I want to make sure I am calculating effective aperture correctly for a lens used with a teleconverter. I think the calculation should be made in order from object to sensor, looking at the objective lens + extension as a black box that the teleconverter acts upon, rather than looking at the whole system as a black box with a single magnification.

Here are the example conditions:

Nominal aperture: f2.8
Objective lens magnification: M=1
Teleconverter: TC=2

I believe the calculation would be:

feff = (finf * (M + 1)) * TC = (2.8 * 2) * 2 = 11.2

This is different than calculating it based on the total magnification MT:

feff = finf * (MT + 1) = 2.8 * 3 = 8.4

So, which is correct, and why?

[rjlittlefield]

The first is correct.

To understand why the first is correct and the second is not, I think it's helpful to recognize that feff_camera = feff_subject*mag_overall in all situations, and then consider how feff_subject changes depending on distance from lens to subject with the teleconverter versus empty extension. (Here I'm using feff_camera to mean the effective aperture as seen by the camera, and feff_subject to mean the effective aperture as seen by the subject.)

To take an example, suppose that you're using a 100 mm f/2.8 lens. Then its aperture will be diameter 100/2.8 = 35.7 mm. With that lens set up to give M=1 by itself, and using thin lens model, it will located 200 mm from the subject, so it will be operating at feff_subject = 200/35.7 = f/5.6. Then with the teleconverter added, the overall magnification becomes 2, and feff_camera = 5.6*2 = f/11.2 .

On the other hand, if you were not using the teleconverter and instead simply added more extension to give mag=2, then the lens would end up located 300 mm from the sensor, only 150 mm from the subject, so it would be operating at feff_subject = 150/35.7 = f/4.2. From there, feff_camera = 4.2*2 = 8.4.

Looking at it this way, you can see that the difference in the two situations is that using the teleconverter gives the same magnification at greater working distance. It's that greater distance with same diameter aperture that results in the larger effective f-numbers.

--Rik

[ray_parkhurst]

Rik...thanks for confirming. The working distance factor nicely explains it...Ray