Why don't eye lenses alter depth perception? 
What it is going to do is bend the rays so that light from infinity "appears" as though it is coinciding with a person's far point. In doing so, it allows the person to see a clear image, without altering their depth perception.

Link to the source.
P.S. This is about the myopic eye.
 A: The human brain puts together a number of different cues to create depth perception. Some examples:


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*The apparent (angular) size of the object. An object that is very far away is brought near a person's far point, but at the same time the magnification is very small, in such a way that the angular size of the object stays the same (so long as the eyeglasses are near enough to the eye). In other words, the image projected onto the retina is the same size with and without eyeglasses. This cue is particularly important for familiar objects that we already know the true size of.

*The angle of convergence of the eyes- if both eyes are pointed at the same object, this gives some information about how far away the object is. This is not really affected by eyeglasses.

*Motion parallax: the apparent movement of stationary objects against the (distant) background. As bought nearby and distant objects are brought closer, no additional motion parallax is seen.


Interestingly, these effects are only negated for eyeglasses that are seated near the eye. Try holding eyeglasses at arm's length and looking through them to see the effects this has on your depth perception.
A: Depth perception is primarily due to binocular vision - the use of two eyes that see at slightly different angles. All predators have binocular vision so that they can pounce/strike accurately. OTOH, most prey species have eyes situate on opposite sides for better threat detection.
See Wikipedia article on stereo vision.
As already pointed out, the optic nerve/brain does a lot of image processing in order to draw conclusions. Relative size is used when other cues are missing. Thus the moon simes to be larger near the earth's horizon than when high in the sky, though if you measure it objectively it willhave the same angular diameter.
