Lateral Shift

​When a ray of light passes through a transparent glass slab, it does not deviate rather it gets laterally shifted. Consider a transparent glass slab of thickness t. Let a ray of light travelling along path OP is incident on the slab at an angle of incidence i. Then, the ray of light gets refracted in the denser medium (glass slab). The ray of light bends towards normal and travels along path PQ such that the angle of refraction is r. Since the two faces of the slab are parallel to each other, the ray of light PQ strikes the surface at an angle of incidence equal to r. Finally, it emerges out of the slab along QR making an angle of emergence equal to i.

lateral shift

Here, the emergent ray QR is parallel to the incident ray OP but the ray has been shifted through a perpendicular distance QN. This perpendicular distance QN is known as lateral shift.

​In rt. angled ΔPQN, \[angle QPN = i-r\] thus, \[sin(i-r)=\frac{QN}{PQ}\] \[∴QN=PQsin(i-r)\text{ __(1)}\] In rt. angled ΔPQM, \[cosr=\frac{PM}{PQ}\] \[PQ=\frac{PM}{cosr}\] \[∴PQ=\frac{t}{cosr}\text{ __(2)}\] From (1) and (2), \[QN=\frac{t}{cosr}sin(i-r)\] \[d=\frac{t}{cosr}sin(i-r)\] This gives the lateral shift. Now, if i=90°, \[d=\frac{t}{cosr}sin(90-r)\] \[d=\frac{t}{cosr}cosr\] \[d=t\] Thus, lateral shift will be maximum if i=90°.

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