Obtian the equation for lateral displacement of light passing through a glass slab.

Explanation

(i) Consider a glass slab of thickness t and refractive index n is kept in air medium. (ii) The path of the light is ABCD and the refractions occur at two points B and C in the glass slab. (iii) The angles of incidence i and refraction r are measured with respect to the normal `N_1` and `N_2` at the two points B and C respectively. (iv) The lateral displacement L is the perpendicular distance CE drawn between the path of light and the undeviated path of light at point C.
In the right angle triangle `triangleBCE,`
` sin ( i - r) = (L)/(BC) , BC = (L)/(sin (i - r) ) " " ...(1)`
In the right angle triangle `triangleBCF,`
` cos (r) = (t)/(BC), BC = (t)/(cos (r)) " " ...(2)`
Equating equation (1) and (2),
` L = t ((sin (i - r))/(cos (r))) " " ....(3)`
(v) Lateral displacement depends upon the thickness of the slab. Thicker the slab, greater will be the lateral displacement. Greater the angle of incident, larger will be the lateral displacement.