# How can lenses with different focal lengths have the same angle of view?

I always assumed that there was a fixed relation between focal length and angle of view. But compare the technical data for the following lenses, all from the same manufacturer:

Why do two lenses by the same manufacturer have the same angle of view at different focal lengths?

They're measuring the first on a crop-sensor camera and the second on a full-frame; specifically for a Canon APS-C sensor, 15mm x 1.6 = 24mm.

Canon does this in general when referring to EF-S vs. EF lenses; see for example How can a 24-70mm and a 10-22mm both be "wide angle" lenses?, which has the same effective answer.

The relationship between focal length and angle of view is fixed, for a given sensor size. More on this at What is “angle of view” in photography?, if it's not already clear.

• How do you know? – user19253 Apr 9 '13 at 10:54
• Because the maths works; 15 * 1.6 (crop factor for Canon APS-C) = 24 :-) Alternatively, because an EF-S lens can be used only on an APS-C camera. – Philip Kendall Apr 9 '13 at 10:59

Canon's EF-S lenses are specifically designed for their APS-C camera bodies. They do not throw an image circle large enough to cover a full frame 36mm X 24mm sensor. For this reason they rate the angle of view for their EF-S lenses based on a sensor size of 22.5mm X 15mm.

All other EF lenses made by Canon are designed to be used on a full sized 36mm X 24mm sensor or film camera, thus the angle of view for those lenses is based on that size focal plane.

The EF-S 15-85mm f/3.5-5.6 IS set at 15mm mounted on a 1.6x crop body has the same angle of view as an EF 24mm f/1.4L II mounted on a full frame camera.