Question

Derive an expression for lateral shift and normal shift. On what factors these depend.

Answer 1

Please find below the solution to the asked query:

Normal shift: Consider the situation shown in the figure.


An object is placed at point O, plane surface CD forms its image (which is virtual) at I1. This image acs as objects for the refraction at the surface EF. Which finally forms an image at I' (virtual). The distance OI is called the Normal Shift. Its value is,
OI = (1−1μ)t
We can derive this as,
Let OA = x, then from the snell's law applied at surface CD,
AI1 = μx
So, the object distance for the refraction at surface EF is BI1 = μx+t. So by applying snell's law at the surface EF,
BI'=BI1μ = x + tμ
So, shift OI' is,
OI' = (AB+OA) − BI' ⇒(t+x) − (x+tμ) = t−tμ ⇒OI'= (1−μ) t

Lateral Shift: Consider the situation shown in the below figure.



The ray MA is incidents at point A on the glass surface at an angle i, as it enters the denser medium, it bends towards the normal at an angle r. And when it comes out of the slab at point B, again it bends away from the normal according to snell's law. Therefore, the emergent ray BN will be parallel to ray MA. If we observe the diagram, we can see that the emergent will be shifted laterally by a distance "d", which is called Lateral shift.

From the ABC,
AB = ACcos r = tcos r; (as AC = t)⇒d = AB sin (i−r) = tcos r(sin i cos r − cos i sin r)⇒d = t(sin i − cos i tan r)

From snell's law,
1 sin i = μ sin r ⇒ μ = sin isin r or sin r = sin iμ⇒tan r = sin i1−sin2i√
Therefore,
d = [1−cos iμ2 − sin2 i√]t sin i
For small incident angle,
d=ti(μ−1μ)
Hope this information will clear your doubts about the topic.

Answer 2

$\large\tt\underline{\red{Answer :-}}$

When a denser medium is kept between two parallel faces inside a rare medium and a ray falls upon one of the two parallel faces reflects into the denser medium and comes out of another surface becoming parallel to the incident ray.

In the successive reflection the deviation at first surface is reversed at second surface but the emergent ray deviates literally.

The distance to what an emergent Ray devited from the direction of incident ray when suffers refraction at two parallel surfaces is called as lateral deviation/ displacement.

The lateral displacement/deviation increase with the increase in

• thickness

• angle of incident

• optical density

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