This page was created in response to a student question regarding depth of field when looking at different kinds of lenses as well as comparing crop-sensor camera bodies and full-frame camera bodies.
I thought I knew the answer but was slightly surprised.
Some background for you - a 'crop-sensor' camera body is one where the sensor is smaller than a traditional 35mm film frame. Typically you see a 'magnification factor' of 1.5 or 1.6 - but do check your manual as your may be different . The effect of that magnification factor is that on a full-frame or 35mm film SLR a 50mm lens is approximately the perspective of how our eyes see. However on a camera like my Sony NEX-6 with a crop factor of 1.6 a 50mm lens 'acts' like its a 70mm lens on a full frame camera like my Canon 5d MkIII.
At 70mm you get into light compression which flattens the subject a touch, as well as decreases the depth of field so the background is slightly more out of focus.
Before I had a full-frame camera, I did use a 1.5x crop-sensor body and did a lot of portraits with a 50mm lens and it looked great. It is very close to using a 75mm lens on a full-frame.
BUT - real world testing tells an even more interesting story.
Here is a series of images I took with my full frame comparing what happens if you shoot at 105mm (the lens I had on the camera) and at 24mm, and then cropped down the 24mm to match the 105mm. I expected them to look fairly similar - the perspective would be similar because objects will be the same distances from the film plane either way, but the 24mm actually had a greater depth of field even though the f stop was the same at a shallow f4.
Then I took one at 24mm but walked in closer to be similar foreground to the 105mm image.
Then I took the same shot from fairly close to the same position (I must have moved a touch when grabbing the different camera) but the perspectives again are similar but very different dept of field. These are shot at f5.6 because of the limitation of the Sony's lens.
Notice the slightly shallower depth of field in the full frame image.
What is 'telephoto compression?'
When shooting any subject you are 1 meter from the subject, and if an object behind the subject is 20 cm further, you could think of the second object as "20 per cent further away from the camera"
But if back up to stand 2 meters away from the subject - the second object is only 10 per cent further away, so it appears to be closer to the subject than when you are closer.
And if you back up another 2 meters (4 meters total) - the second object is now only 5 per cent further away than the subject.
Overall the ratio of difference between the subject and second object and the distance to the camera gets smaller the further the camera is away. From the earth, the moon looks quite a long distance away, but if you look at the earth and moon from Pluto, the earth and moon look pretty close together.
What a telephoto lens does is let you stand further back and 'crops down' the image compared to standing really close with a wide angle lens. As well, because of how the optics work in a telephoto lens, the longer the lens is, the shallower the depth of field will appear. The exception is when you get out to long distances such as near the horizon, or nearer infinity. The further from the lens you focus, the depth of field will increase.
See the lesson on Depth Of Field for exercises to explore what your can achieve with depth of field.