does crop factor affect the actual f-stop?

[emanresu]

With small sensors that has crop factors n>1, you "gain" some more focal length by (n - 1)x lens-focal-length.  But at the same time, do you also lose the amount of light hitting the sensor, and therefore affect the actual f-stop?  Suppose a particular lens at a certain focal length and a certain aperture lets in x amount of light to hit a full-size sensor, if all conditions remain the same but the sensor is switched to a smaller one with crop factor of n, don't you get only x/n amount of light?

I don't recall reading about this anywhere, for normally when people mention crop factors, they only talk about the gaining in focal length, but not the loss of light.  So is this true? If so, then if I mount an EF lens on an EF-S body, and set the aperture to f, it will be equivalent to a f-prime which is slightly higher than f, no?

If this is false, could someone (bob?, keith?) be patient with me and explain it to me why it doesn't affect the aperture?  Thanks.

[Tallyther]

I don't have any test experience but I can offer some comments from the theoretical physics/mathematics side. 

We know there are combinations of larger f-stops and ISO that are equivalent to smaller fstops with higher ISOs.  All this is a measure of light per unit area.  So as is always the case, nothing is simple here and we need to define what is it about the sensor area and position that's important.  Some crop factor sensors have more pixels than full format sensors.  So as long as we are comparing only on a basis of units of light per sensor area as defined by pixel size (which also varies in arrangement, sensitivity, and focal distance, but given all is equal) then there is no net effect.  The f-stop is fixed period! 

Using your analogy then you must ask if you have a lens that requires more asherical correction or is of a very short focal length as opposed to long, does it affect f-stop? Or if the glass is not as good, does it affect the f-stop?  Again, F-stop is fixed and everything else around it pivots.  It might be more appropriate from a theoretical design perspective to ask "given a set f-stop, what effect does crop factor have on the light getting to each pixel and arrangement, due to additional required aspherical correction?  I think the conclusion one might reach depends on which side of the focal point you start.

[Bob Atkins]

I've written an article that addresses most of the issues around crop sensor cameras and lenses, including "digital multipliers" and effects on aperture. You can read it here:

http://www.bobatkins.com/photography/tutorials/crop_sensor_cameras_and_lenses.html

The answer to your question is that the f-stop of the lens does not change when you mount it on a crop sensor camera. All you are doing is cropping the image that the lens produces. The brightness of the image obviously doesn't change when you crop it, so croppoing has no effect on image brightness. Since the brightness is related to the f-stop, the f-stop obviously doesn't change either.

The key here is that you don't change the focal length of the lens when you mount it on a crop sensor body. What you change is the angle of view. Since we're used to thinking of angle of view in terms of 35mm focal length, the "digital multiplier" is just a quck way to get an impression of the field of view of the lens. So on a full frame camera a 28mm lens is a wideangle, but a 24mm lens on a crop sensor is still a 28mm lens, it just gives a narrower angle of view. The "digital multiplier" is just a quick way to see that, so you can say that the lens woul have the same FOV as a 45mm lens on a crop sensor camera (28 x 1.6 = 45) EVEN THOUGH IT'S STILL A 28mm LENS.

[emanresu]

thanks for the answers, and Bob, I am sorry that I missed your article.  I should've looked this up before asking the question - luminosity is defined as candele per square m, so it also clearly says that sensor size doesn't change the brightness.

[klindup]

A very good article Bob.  I think that some of the confusion comes from the loose way we use terms.  We talk about a wide angle lens but not a narrow angle lens.  We call those telephotos whereas my understanding has been that a telephoto lens was a lens whose physical length was less than its focal length, in other words a method of construction.  Some wide angle lenses are actually reversed telephoto lenses. 

Regardless of angle of view or focal length it was always my understanding that the diameter of the front element or in the case of a mirror or catadiptric lens that determines its light gathering capabilities.  The focal length determines the area from which it gathers light and hence how much light is passed back to the sensor/film or eyepiece in the case of a telescope.

[emanresu]

Sorry for digging up this thread again, Bob.  I read the article you wrote on crop factor vs focal length, and it made everything very clear (thank you!).  However, one question remains.  I some how got the impression (probably read it from some online text, maybe due to my own erroneous interpretation of the text) that while a 50mm EF lens on an cropped-sensor body (x1.6) will give the FOV equivalent to 80mm EF on a full-frame body, a 50mm EF-S lens will give the same FOV on the cropped body as a 50mm EF on a full-frame body, reason being EF-S lenses are adjusted for the cropped sensor.  After having read your article I know this most likely makes no sense, because as you said in the article, the focal length of a lens is the focal length of a lens.  But then why does Canon come up with the EF-S lenses?  Thanks.

[Bob Atkins]

You have been misinformed. If there was an EF-S 50mm lens it would give EXACTLY the same view on an APS-C crop sensor camera as any of the full frame EF 50mm lenses do. EF-S lenses do not have their stated focal length "adjusted" for the crop factor. The only difference would be that an EF-S 50mm lens would have a smaller image circle than an EF 50mm lens. Large enough to cover a crop sensor, but too small for a full frame sensor.

[emanresu]

I see.  Thank you for all the clarifications and explanations, Bob.  Finally I am no longer confused

[KeithB]

And, EF-S lenses have a mount that won't attach to a Full-Frame Camera.  This is because the smaller mirror in the 1.6X cameras can allow the lens to project farther back into the camera body.  If you put this lens on a FF camera, the mirror might whack the back of the lens.  Ouch!