We’ve shared this same topic here a couple of times before, but Jay P. Morgan of The Slanted Lens created this video lesson showing some examples of how profound of an impact your focal length choice can make.
Here’s one of the series he shows, shot using lenses ranging from a 200mm telephoto to a 20mm wide angle:
The model’s appearance on either end of the spectrum isn’t very appealing, huh? That’s why portrait lenses usually have focal lengths somewhere in the middle (in 35mm photography, at least).
Check out what Wikipedia says about the subject:
Classic focal length is in the range 80–135mm on 135 film format and about 150-400mm on large format, which historically is first in photography. Such a field of view provides a flattering perspective distortion when the subject is framed to include their head and shoulders. Wider angle lenses (shorter focal length) require that the portrait be taken from closer (for an equivalent field size), and the resulting perspective distortion yields a relatively larger nose and smaller ears, which is considered unflattering and imp-like. Wide-angle lenses – or even fisheye lenses – may be used for artistic effect, especially to produce a grotesque image. Conversely, longer focal lengths yield greater flattening because they are used from further away. This makes communication difficult and reduces rapport. They may be used, however, particularly in fashion photography, but longer lengths require a loudspeaker or walkie-talkie to communicate with the model or assistants.
Note that all this has to do with using different focal lengths while keeping the subject at the same size in the frame. This means that you’re moving your camera closer and further away from the subject with each new focal length. As John Cornicello explains in this tutorial, keeping the camera fixed and cropping to achieve the same framing would yield nearly identical photos, regardless of focal length.
How Lens Focal Length Shapes the Face & Controls Perspective [The Slanted Lens]