Lateral Shift
When a ray of light is incident on a glass slab, the emergent ray coming out of the slab will be parallel to the incident ray. The perpendicular distance between the direction of incident ray and emergent ray is called the lateral Shift. It is denoted by d.
Expression for Lateral Shift
Consider a glass slab WXYZ of thickness t, where a light ray OA is incident on the glass at point A making angle of incidence as i and is refracted making angle of refraction r through the glass slab and emerges out from the point B on the glass slab i.e. AB is refracted ray. Here incident ray is produced and BQ is the lateral shift according to its definition.
<N2AQ = <OAN1 = i<N2AB = r
<BAQ = i – r
From ΔABQ,
Sin (i-r) = BQ / AB
or, AB = AB sin(i-r) ………. (i)
From ΔABN2, we have
Cos r = AN2/ AB = i / AB
or, AB = t / cos r …... (ii)
From equation (i) and (ii),
BQ = t sin (i-r)/ cos r
Special cases,
When i = 90,
D = t sin (90-r) / cos r
Therefore, d = t
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