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[Phys-L] Refraction Implications

Two measurements of refraction give apparently contradictory results.

A parallax measurement from air into a denser refractive material shows
that distance to the back of the material appears to be shorter than the
actual length.
A time of flight measurement of a laser pulse indicates that the distance
to be back appears to be longer.

I made a video to demonstrate this:

Before you send me refraction diagrams, yes I understand that all of these
observations are correct. Light slows down in proportion to the index of
refraction. Light bends according to Snell's Law. I understand those
principles. Frankly, I'm enjoying the contradiction between the two
measurements above. Oftentimes at a point of contradiction like this there
is a deeper understanding to be gleaned. Help me out there. To what new
insights might this lead?