Refraction and Dispersion of Light due to a Prism
A prism is a portion of a transparent medium bounded by two plane faces inclined to each other at a suitable angle.
Angle A between the two refracting surfaces ABQP and APRC is called the angle of prism.
A ray of light suffers two refractions on passing through a prism.If KL be a monochromatic light falling on the side AB, it gets refracted and travels along LM. It once again suffers a refraction at M and emerges out along MN. The angle through which the emergent ray deviates from the direction of incident ray is called angle of deviation 'd'
Relation between Refractive index (m) Angle of Prism (A) and angle of deviation (d)
Draw LO and MO at L and M respectively. Extend KL and MN to meet at P.
i.e. d = i1 r1 + i2 r2
d = i1 + i2 (r1 + r2)
(exterior angle is sum of interior opposite angles)
In the quadrilateral ALOM
(From Snell's law)
As the angle of incidence is increased, angle of deviation 'd' decreases and reaches minimum value. If the angle of incidence is further increased, the angle of deviation is increased. Let dm be the angle of minimum deviation. The refracted ray in the prism in that case will be parallel to the base.
For minimum deviation position the incident ray and emergent rays are symmetrical with respect to the refracting surface and LM is parallel to BC.
i1 = i2 = i
and r1 = r2 = r
2r1 = A , r1= A/2
dm = 2i1 - 2r1
dm = 2i1 - A
or 2i1 = dm + A
From Snell's Law
This is the Prism formula when the prism is in the minimum deviation position.
For thin prism A is very small and if the light is incident at a small angle then i1, r1, r2, i2 are so small.
That d= (m-1) A
