Question

Effect of lateral deviation on light on changing thickness of glass slab

Answer 1

Suppose your slab has a certain thickness, say dd. From Snell's law about refraction, calling θiθi the angle between the incoming ray and the normal to the surface, nini the refractive index of the medium outside the slab, nmnm the refractive index inside the slab and θmθm the angle between the ray in the slab and the normal to the surface:

nmsinθm=nisinθi

you can derive the angle θmθm:

sinθm=ninmsinθi

Then, from basic trigonometry, you know that:

sin2θm+cos2θm=1 ⇒ cosθm=root1−sin2θm

and, with dd as defined and ll length of the path of the ray inside the slab, you can write:

d=l⋅cosθm ⇒ l=dcosθm

Calling xx the lateral displacement you are asking for:

x=l⋅sinθm

By substituting in this equation, you can get your result as an expression of the angle of incidence, the refractive indexes and the thickness of the slab.

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