CBSE Class 10 Answered
Lateral displacement is the perpendicular distance between incident ray and emergent ray , when light ray is refracted through transparent slab as shown in figure.
In figure lateral displacement is BC = d .
From right ΔABC we knaoe d = AB sin(i-r)
AB = t / cos (r)
where i is angle of incidence, r is angle of refraction and t is thickness of slab
Hence lateral displacement d = [ t sin (i-r) ] / cos (r) ..........................(1)
In special case where angle of incidence i and angle of refraction are small
sin( i - r ) ≈ ( i - r ) and cos (r) ≈ 1
Hence , we rewrite eqn.91) as d = t ( i - r ) ........................(2)
By law of refraction = sin(i) / sin(r) = i / r = μ
where μ ios refractive index of material of slab
Hence eqn.(2) becomes
Hence factors affecting lateral displacement are (i) thickness of slab , (ii) angle of incidence and (iii) refractive index of material.
lateral displacement d is directly proportional to slab thckness t
lateral displacement d is directly proportional to angle of incidence i
lateral displacement increases as refractive index μ increases