How to derive lateral shifting formula?

Answer 1

When a ray of light from a medium is incident on another medium with different optical density, the ray bends due to refraction. The perpendicular distance between the emergent ray and the incident ray is called the lateral shift. The angle which the incident ray makes with the normal is called angle of incidence denoted by 'i' and the angle made by the refracted ray with the normal is called the angle of refraction denoted by 'r'. Lateral shift is given by the formula:- Where t is the thickness of the glass slab, i is the angle of incidence and r is the angle of refraction

Answer 2

The lateral shifting formula in optics, which describes the displacement of a ray of light as it passes through a transparent medium, can be derived using principles of Snell's Law and trigonometry. By considering the angles of incidence and refraction at the interface between two media, and using the fact that the displacement is proportional to the thickness of the medium and the difference in refractive indices, the formula for lateral shift can be derived.