Why does a 2x TC lose 2 stops?

[JumboShrimp]

Time for the day's stupid question:

It is a known fact that all 2x teleconverters lose 2 stops of light, and all 1.4x TCs lose one stop of light. Why? What if the glass in the TC was twice as large? ... it would let in more light, therefore the light loss would be less. Now I realize this logic is somehow flawed, but I can't reason why. Anyone?

 

[Loswr]

Simple...the f/number is the ratio of the focal length to the physical maximum diameter of the iris diaphragm (aperture), both in millimeters. A TC increases the focal length, but has no effect on the diameter of the iris diaphragm. For example, a 200mm f/2 lens has an iris diaphragm that is 100mm in diameter. Put a 1.4x TC behind it, you have a 280mm lens that still has a 100mm physical aperture. 280/100 = f/2.8, one stops slower than f/2. Put a 2x TC behind it, you have a 400mm lens that still has a 100mm physical aperture. 400/100 = f/4, two stops slower than f/2.

 

[jrista]

Time for the day's stupid question:

It is a known fact that all 2x teleconverters lose 2 stops of light, and all 1.4x TCs lose one stop of light. Why? What if the glass in the TC was twice as large? ... it would let in more light, therefore the light loss would be less. Now I realize this logic is somehow flawed, but I can't reason why. Anyone?

Because stops are RELATIVE. Stops are ultimately based on a ratio, such as f/4. That 'f' stands for 'focal length', and it's a simple mathematical formula. So, it really means 'focal length divided by four'. If you have a 400mm f/4 lens, your entrance pupil (the physical aperture as viewed through the front of the lens at "infinity") is 100mm in diameter. The f-ratio is actually determined by dividing the focal length by the entrance pupil diameter, so the 'f/4' really comes from 400mm/100mm, which equals 4.


If you slap on a 2x teleconverter, you are adding on what is effectively a magnifying glass to the end of your lens. In this case, it magnifies your subject by a factor of two, which is the same as doubling your focal length. So, now you have an 800mm lens. Thing is, the lens did not get wider...it's the same diameter, which means it has the same entrance pupil. The entrance pupil of the lens, when observed from "infinity", is still 100mm. That means that your f-ratio is now 800mm/100mm, which equals 8. You've lost two stops of light (f/4 -> f/5.6 -> f/8).


I'm sure there is still the same question, though...why? First, the entrance pupil is ultimately what determines the amount of light that will produce the image circle at the sensor plane. The AREA of the opening in the diaphragm, to be specific, is what determines the amount of light. So, a 100mm entrance pupil means you have pi(d/2)^2 area, or 7854mm^2 circular area. Attaching a TC to a lens is adding a magnifying glass to the BACK of the lens. You've already limited the amount of light, since by the time it reaches the TC, it's already passed through the aperture. A 2x TC is effectively taking the center portion of circle of light produced by the aperture, 1/4 the area or 1964mm^2, and enlarging it to the same 7854mm^2 (which is then projected by the rest of the optics in the TC to the standard image circle size for the camera, say 44mm diameter for FF; it's really a bit more complicated than that, but for casual conversation sake).


It's taking a smaller quantity of light from the center area of the image circle and spreading it out over a greater area. In other words...one quarter the quantity of light spread out over four times the area that light initially covers results in two halvings of the intensity of light at any given pixel.

 

[chromophore]

Without going into the details of how a teleconverter affects focal length and its relationship to entrance pupil and f-number, the fundamental idea is that a teleconverter essentially takes an image formed by the primary lens and magnifies it.

Think about a slide projector, that outputs a fixed amount of light from the bulb, passing through the slide, through the lens, and onto a wall. The resulting image is a certain size. If you now move the slide projector back so that the image is twice as wide and twice as long, it is now four times the original area (2 x 2 = 4). The same amount of light is distributed over 4 times the area, which means that the image is only 1/4 as bright. This is a 2-stop decrease in light intensity per unit area. A 2x teleconverter does essentially the same thing, only that the image is magnified not by increasing the distance between lens and sensor, but by placing additional glass between--just like a simple convex magnifying glass does.

A 1.4x teleconverter loses only one stop because the scaling factor is the square root of 2, thus the area of the magnified image is only twice that of the original; thus the image 1/2 as bright as the original, which is 1 stop.

The reverse principle also applies for what might be called wide-angle converters--these include the adapters that we have more recently seen developed for using 135 format lenses (e.g., EF lenses) on smaller sensors on mirrorless cameras. Their design permits the incorporation of additional optics that concentrates the image circle, so that two effects occur: the focal length becomes reduced, and the image gets brighter, because the same amount of light is falling on a smaller area.

 

[JumboShrimp]

Wow! All good answers. Thanks everyone!

 

[AcutancePhotography]

I don't think that was a stupid question at all. We got some good answers that educated some of our readers. I am sure that others besides you had wondered about this.

We need more posts like this.

Now that I got some actual learnin', I need to leave this website and visit Canonrumors.com where I am sure there is some entertaining fight to read about. ;D

Oh, this thread was on Canonrumors? (rubbing eyes)????

 

[Loswr]

In the discussions of TCs affecting 'brightness', it's important to remember that the change to f/number with a TC affects not just light intensity, but also depth of field. A 300mm f/2.8 with a 2x TC behind it is a 600mm f/5.6 lens, with the DoF of an f/5.6 lens.

 

[Canon1]

In the discussions of TCs affecting 'brightness', it's important to remember that the change to f/number with a TC affects not just light intensity, but also depth of field. A 300mm f/2.8 with a 2x TC behind it is a 600mm f/5.6 lens, with the DoF of an f/5.6 lens.

Here is an example as to why this matters: If you normally shoot a subject (say a bird) from 20 feet with a 200f2.8 lens you have a working depth of field of .5 feet. By adding a 2.0x you can now shoot that same bird from 40 feet to achieve the same field of view... however your new combination is a 400mm f5.6 with a depth of field of 1 foot. While you have more "reach" you will also suffer a greater depth of field resulting in an out of focus back ground that is not as smooth as shooting 200mm f2.8 from 20 feet. So your effective focal lenght doubled... but so did your depth of field, which can be beneficial in some cases.

 

[westr70]

I appreciate the information provided by the participants. I learned a lot by reading these comments. Thumbs up to the OP.

 

[meywd]

Great info, thanks for the question and the answers, i guess information like this need a knowledge base forum, which is moderated.

 

[heptagon]

The reverse is also true: A 0.5x TC gains 2 stops.

Those are usually sold as speed boosters to use a full frame lens on a crop camera. If i recall correctly, some lens designs with a wide angle and a large aperture have such an element built in.

 

[AcutancePhotography]

The reverse is also true: A 0.5x TC gains 2 stops.

Wow, I have never heard of that. That's two learnin's I got from one thread.

 

[3kramd5]

The reverse is also true: A 0.5x TC gains 2 stops.

Wow, I have never heard of that. That's two learnin's I got from one thread.

http://www.metabones.com/products/?c=speed-booster

 

[Steve Balcombe]

In the discussions of TCs affecting 'brightness', it's important to remember that the change to f/number with a TC affects not just light intensity, but also depth of field. A 300mm f/2.8 with a 2x TC behind it is a 600mm f/5.6 lens, with the DoF of an f/5.6 lens.

Here is an example as to why this matters: If you normally shoot a subject (say a bird) from 20 feet with a 200f2.8 lens you have a working depth of field of .5 feet. By adding a 2.0x you can now shoot that same bird from 40 feet to achieve the same field of view... however your new combination is a 400mm f5.6 with a depth of field of 1 foot. While you have more "reach" you will also suffer a greater depth of field resulting in an out of focus back ground that is not as smooth as shooting 200mm f2.8 from 20 feet. So your effective focal lenght doubled... but so did your depth of field, which can be beneficial in some cases.

This is incorrect in one important detail. The amount of distant background blur actually remains the same, because it depends only on the entrance pupil size which hasn't changed of course. More depth of field on the subject and equal background blur means a potentially sharper subject therefore stronger subject separation.

 

[3kramd5]

Time for the day's stupid question:

It is a known fact that all 2x teleconverters lose 2 stops of light, and all 1.4x TCs lose one stop of light. Why? What if the glass in the TC was twice as large? ... it would let in more light, therefore the light loss would be less. Now I realize this logic is somehow flawed, but I can't reason why. Anyone?

What a TC effectively does is magnify. It spreads a constant amount of light over a larger area. So no, if it were bigger, it wouldn't let in more light.

 

[AcutancePhotography]

The reverse is also true: A 0.5x TC gains 2 stops.

Wow, I have never heard of that. That's two learnin's I got from one thread.

http://www.metabones.com/products/?c=speed-booster

So they are only used with mirrorless cameras? That's probably why I never heard of them. Still interesting though. Thanks for posting it.

 

[3kramd5]

The reverse is also true: A 0.5x TC gains 2 stops.

Wow, I have never heard of that. That's two learnin's I got from one thread.

http://www.metabones.com/products/?c=speed-booster

So they are only used with mirrorless cameras? That's probably why I never heard of them. Still interesting though. Thanks for posting it.

I've not seen one that is, for example, EF to EF. It would be kinda cool I suppose to use one to brighten up and widen EF lens for use on a crop body. Maybe there's something out there.

 

[mnclayshooter]

I tried describing this to a friend of mine (not really into photography but curious about some of the equipment in my kit)...

I think the one thing that resonated as a visual description was to describe a lens like a funnel. The objective lens is the open "top" of the funnel... That's where the light is gathered. It is constricted through the tapering of the funnel (the columnation of light inside the barrel of the lens) and then focused on the sensor (your eye) at the narrow throat-end of the funnel. Simply adding more length of tube onto that end of the funnel doesn't allow you to add more light. Widening the objective lens or widening the throat would possibly allow it though.

Take it for what it's worth... it got the point across, whether technically correct or not. 8)

 

[chromophore]

I've not seen one that is, for example, EF to EF. It would be kinda cool I suppose to use one to brighten up and widen EF lens for use on a crop body. Maybe there's something out there.

Such an adapter would not be practical for two reasons: first, because the image circle is reduced in proportion to the conversion scaling factor, and because most if not all EF lenses are designed to only project an image circle roughly large enough to cover the 24x36mm imaging sensor, the result of such a converter in an EF-to-EF system would be large sections of black, unexposed sensor in the image periphery.

The second reason applies even if the system was intended to adapt an EF lens to an EF-S DSLR: physically inserting the converter would likely require a shorter backfocus distance, thus impinging on the mirror box. Unlike a teleconverter, wide-angle converters are typically designed to be closer to the image plane--this is how they achieve the focal length reduction. So, for a mirrorless system with a lens that was designed to work on a mirrored system, there's enough space to insert something in between. But with a system that has a mirror box, such a converter would be unlikely to have satisfactory performance.

 

[3kramd5]

Such an adapter would not be practical for two reasons: first, because the image circle is reduced in proportion to the conversion scaling factor, and because most if not all EF lenses are designed to only project an image circle roughly large enough to cover the 24x36mm imaging sensor, the result of such a converter in an EF-to-EF system would be large sections of black, unexposed sensor in the image periphery.

Naturally, but note that many people don't mind cropping (D800/600, probably many sony models will do it in camera), and may be willing to give up peripheral pixels in exchange for brightness.

That said, there likely isn't a major market for it.