1) Lateral shift refers to the perpendicular distance between the original direction of an incident ray of light and the emergent ray after refraction through a medium. 2) The expression for calculating lateral shift is d=t sin(i-r)/cosr, where t is the thickness of the medium, i is the angle of incidence, and r is the angle of refraction. 3) Lateral shift increases with increasing angle of incidence, and is at a maximum when the angle of incidence is 90 degrees and equals the thickness of the medium.

1. LATERAL SHIFT AND ITS VARIANCE
WITH ANGLE OF INCIDENCE

2. Refraction of light
The phenomenon of bending of light as it moves from one medium to
another is called refraction of light.
The laws of refraction are:
 The incident ray, refracted ray and normal at the point of incidence all lie
at the same point.
 The ratio of sine of angle of incidence to the sine of angle of refraction is
always constant. This constant is known as refractive index.
i.e. µ=
sin 𝑖
sin 𝑟
This is often known as Snell's law

3. Lateral shift
 The perpendicular distance between the original direction of incident ray and
emergent ray and emergent ray is lateral shift.
Lets consider a ray of light AO is incident on air-glass interface making angle of
incidence ∡AON’=i which refracted in glass medium making angle of refraction
∡N’OB and finally emerges out of the glass along BE making angle of emergence
∡M’BE=e
If incident angle AO is produced, then it will be parallel to the emergent
Ray BE. A perpendicular drawn from the point of emergent to the original direction
of incident ray measures the lateral shift i.e. BP=d is the lateral
shift.

5. From figure, ∡BOP= i – r
In triangle BOP,
sin 𝑖 − 𝑟 =
𝐵𝑃
𝑂𝐵
-------(1)
Again, in triangle N’OB,
cos 𝑟 =
𝑂𝑁′
𝑂𝐵
or, OB=
𝑂𝑁′
cos 𝑟
------------(2)
From equation 1 and 2, we get
sin 𝑖 − 𝑟 =
𝐵𝑃
𝑂𝑁′
cos 𝑟
or, BP =
𝑂𝑁′ sin(𝑖−𝑟)
cos 𝑟
If ON’=t be the thickness of glass slab, then
d=
𝑡 sin(𝑖−𝑟)
cos 𝑟
This is the required expression for lateral shift.

6. Cases:
1) If i=0° then, r=0
So, d=0
2) If i=90° then ,
d=t
Thus, when the angle of incidence is 90° , lateral shift is maximum and is equal to the
thickness of slab.
If a graph is plotted between angle of incidence with lateral shift it is obtained as
shown below.
The graph shows that, lateral shift increases in angle of incidence and becomes
maximum when the angle of incidence is 90°