CBSE Class 10 Answered
How does the lateral displacement of light ray vary? on what factors it depends? directly proportional or inversely?
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
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