I'm reading that a 50mm lens is recommended as a first prime lens for DSLR owners as it's supposed to give a 'natural' perspective, but when used on (most) DSLRs, the view is cropped, as if you were zoomed in by 1.5-1.6x, so it's more of a telephoto lens when used on a DSLR. I've also read however that the 50mm lens gives the same perspective on a DSLR and a 35mm, and shouldn't really be considered to be 'equivalent' to an 80mm lens as the crop factor isn't really a magic focal length changer.
Can someone explain how the image is different from (for example) a 50mm lens on a DSLR and an 80mm lens (assuming 1.6x crop factor) on a 35mm camera?
Answer
You can find detailed definition of Crop Factor in Wikipedia there is also a good explanation on dpreview site where it is referred to as "Focal Length Multiplier"
In short in your scenario if you have one full frame camera (crop factor 1) with 80mm lens and a second camera with 1.6 crop factor and 50mm when taking photos from the same position you will get the same frames (80 x 1 = 50x1.6 = 80)
That does not mean however that the photos will be identical. The depth of field for example if shooting with the same aperture will be different as it is still dependent on the (actual) focal length of the lens, that is the reason why people who are interested in achieving shallow depth of field tend to use full frame cameras.
Also the camera with crop factor 1.6 has a smaller sensor (see crop factor definition) - so assuming the both have same resolution say 10 Mega Pixels, and use the same technology the full frame camera will have bigger pixels, each would capture more light and that would usually translate into better high iso performance and better dynamic range.
More details in linked articles:
Please Note
Crop Factor is sometimes referred as "Field Of View Crop" ("FOV Crop"), "Magnification Factor", "Focal Length Factor", or "Focal Length Multiplier".
As pointed out correctly by Rowland Focal Length Multiplier and other terms that mention focal length are not correct and can be confusing as the focal length does not really change here. Those terms are however still being used in some camera reviews or specifications.
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