Relationship

[EIRE2003]

The relationship between real depth, apparent depth & refractive index.
Is it, n=real depth/apparent depth, where n is the refractive index of the medium?

[Doc Al]

Yes, assuming you are looking perpendicular to the surface of the medium (refractive index n) from vacuum or air (refractive index 1). An object in that medium looks closer to the surface than it actually is due to refraction.