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So, I mount a 200mm lens on my Canon 450D. It effectively becomes a 320mm lens. Is this the equivalent of 320mm on a full frame camera? That is, from what I've figured out I get an equivalent field of view but nothing I've read is indicating that I get the magnification to go along with it.

So as my question says in the title, does my crop sensor camera really turn my lens into a longer one (in terms of magnification), or does it just look like it based on the reduced field of view I get?

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2  
Related: photo.stackexchange.com/questions/139/… –  coneslayer Apr 27 '11 at 11:30
1  
And also photo.stackexchange.com/questions/2536/…. There's a lot of questions which come close, but this is confusing enough to people that I think we can support multiple questions approaching the issue from a different angle. –  mattdm Apr 27 '11 at 11:58

4 Answers 4

up vote 26 down vote accepted

The lens does not actually turn into a different focal length, since that's a real, physical property of the optics that can't be changed without more optics. So from that point of view, the answer is a definitive no.

However, when you get to the question of is it effectively the same in terms of magnification, the answer is "pretty much, given some assumptions."

A key assumption is that you're printing at the same size. That means: you're increasing the magnification of the image from the smaller sensor. If you print at sizes different by the same ratio of the crop factor, you get exactly the same result as if you just took a full-frame photo, printed large, and then cropped out the middle.

So, if you print your full-frame picture at 12×9", and print your crop-factor picture at 7.5×5.6" (for Canon; 8×6" for others, or 6×4.5", or whatever), and then chop down the full-frame print to match, they'll be roughly the same.

"Roughly" comes in because, of course, the actual sensors won't be equivalent in image quality. (The crop-factor print may have larger resolution, but from denser photosites, depending on the technology generation used in each camera.)

Blowing up that cropped image — either from the full-frame cropped print, or from the cropped sensor — has two effects which are very like changing the focal length. And these two things are the most visible effects of changing focal length — field of view, as you've noted; and depth of field, which changes exactly as if you'd adjusted the f-stop by the amount of the crop.

If you've ever used a point and shoot camera with "digital zoom", that's what's actually going on. It's cropping the photo and then expanding it. From a practical point of view, zoom is indistinguishable from cropping. But of course, that raises the spectre of decreased image quality — we all know that digital zoom can be awful. The answer is simply that sensor technology is really very good, and amazing, excellent results can be produced at even large print sizes even with a 1.5 or 1.6× crop — but if you do want to go larger with your prints, eventually you need a larger sensor. And, equivalently, if you want to zoom in more, you can do that with more cropping, but eventually, you need actual higher-focal-length glass.

Note that this doesn't address macro shooting. I don't really do any of that, so I'll let someone else handle that aspect of the question — which I think is well-addressed here: Does a camera's crop factor apply to the magnification of macro shots?

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Thanks for the description. I'd never considered the crop factor in these terms. I'd also never considered what "digital zoom" is actually doing. This is probably the best justification for getting a full frame I've read. +1 –  Mike May 4 '11 at 10:40
    
@Mike: yeah, there's pretty much no real downside to a full frame camera except for size, weight, and cost. (See photo.stackexchange.com/questions/3986/… for more....) –  mattdm May 4 '11 at 12:06
    
I did find another justification for getting an EOS1D - if you forget your hammer, you can use one of these to bang in your tent pegs. It's just that it makes for a really expensive hammer that's all... –  Mike May 5 '11 at 4:56

The crop sensor does not change any property of the lens - but by seeing just the center of the image it makes it look like everything is multiplied by the crop factor.

The focal length does not change - but by looking only at the center of the image makes it look similar to what you get by using a longer lens.

The magnification also does not change, a marco lens with 1:1 magnification will still have 1:1 magnification (object size in reality = object size on sensor) but now that the sensor is smaller the object on the image will be 1.6 bigger, for example:

Full frame:                              Crop Sensor:
+-sensor----------------+
|                       |
|   +-subject--------+  |                +-subject--------+
|   |                |  |                |   +--sensor--+ |
|   |                |  |                |   |          | |
|   |                |  |                |   +----------+ |
|   +----------------+  |                +----------------+
+-----------------------+        
subject is entirely inside image         subject is exactly the same size and 
                                         position but is now larger than image

The subject projection on the sensor is exactly the same size (lens magnification didn't change) but it take a larger area of the image because the sensor is smaller.

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8  
+1 for the ASCII drawing –  Sean Apr 27 '11 at 16:06
    
@Sean: When I saw the ASCII art, I immediately felt a strong urge to post that very comment –  Anto Apr 27 '11 at 17:11
    
Thanks for the added bit of info regarding macro photography. It added to what mattdm has said. +1 –  Mike May 4 '11 at 10:45

The depth of field, as defined by the aperture, also does not change. The only reason it is larger (more in focus) than on a full frame sensor, is because of the cropping factor, the person must move backward (or zoom out) to achieve frame something the same within the image.

In other words, if you had a full frame body setup with a 50mm lens at F/1.8 aimed at a subject 2m away then replace the camera with a crop sensor body but use the same lens and position (2m), the depth of field will still be exactly the same, but you will see less of the image seen in the full frame body (crop).

As the depth of field increases with focus distance, and due to the fact that you must move back to frame the same composition, your focus distance on the crop body is increasing, effectively increasing the depth of field to something larger than the full frame image's depth of field.

enter image description here

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Or stand in the same place, and crop off the edges of the full-frame image, and then display both at the same size. :) –  mattdm Nov 8 '11 at 4:32
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Yep. Exactly the same composition (disregarding difference in sensor quality). Snip snip! –  Nick Bedford Nov 8 '11 at 4:49

I once asked this and got many confusing answers, but in the end I understood it, and I will try to explain it as simply as I can:

  1. Nothing about the lens is ever changed. It is not a Transformer after all, so every property of it remains the same.

  2. A photo taken with an APS-C camera is like taking photo on a Full-Frame camera and then printing it out, and then you crop it to make it smaller by chopping off a portion from all four sides.

If you understand (1) and (2), you will immediately understand that nothing has changed, not even Depth Of Field, not focal length, etc.

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