Let me assume that the index of refraction in air is 1.

The index of refraction of ebonite was found by Profs.

Well, that won't give you the depth, but it could give you the index of refraction.

You could also estimate the index of refraction by measuring the angular distance between the head and body.

Their minds had the same index of refraction, so that thoughts flashed back and forth between them effortlessly and without distortion.

Oh, let's say the index of refraction for water is 1.33 - that's important for the plot below.