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Let's say I am at a gym and need to take a photograph of myself. I can hold out my hand with my D80 to take a picture of myself but the perspective compression would make my face look like Mr. big nose.
If I take a picture of myself looking to a mirror with D80 at hand. Would that be 2x the distance between the mirror and camera for perspective compression reduction which would give me realistic face proportions?
The image you see in the mirror is twice the distance from the mirror plane to the observer which will help with compression when taking a selfie. Your image will be mirrored if taking a picture of the mirror image. You may want to flip the image in post processing.
Go in to a dressing room and orient the mirrors so they are almost aiming towards each other and look at the repeated pattern of reflections that get smaller and smaller. You can also do this if your eyes are just above a handheld mirror aiming at a wall mounted mirror.
You can visit the Wikipedia page which gives the mirror equation showing this relationship.
If an object is located some distance in front of a mirror, its reflection is seen at the same distance behind the mirror.
So, if you stand 3m in front of the mirror, hold your camera 0.5m in front of your body, the result is:
If you hold the camera close to your eye, you simply get twice the distance to the mirror.
When taking a selfie, distance camera -> person = arm length
When taking a photo facing a mirror,
distance camera -> person =
distance camera -> mirror +
distance mirror -> person
The second longer path helps for a better body proportion rendering.
