Question

what are the factors on which the lateral shift depends when light passes through a glass lab

Answer 1

It depends on the angle of incidence, refractive index and thickness of the medium...

It is directly proportional to the thickness of the slab and the angle of incidence..

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Answer 2

It depends upon the thickness of the slab, angle of incidence , angle of refraction and since these two angles are related by  refractive index we can equally say that lateral displacement depends upon refractive index.