Refraction of Light Through Prism

Ordinary white light, as we know, is a superimposition of waves having wavelength throughout the visible spectrum

Prism is that optical instrument which splits this white light into its constituent wavelengths

A prism dispersing white light into its composite wavelengths or colours

This breaking up of white light inside a prism happens through refraction at the prism-air interface

Let us now understand some mathematical relations incorporating Refraction of light through a prism

We consider the principal section of a prism,

Let two normals and be incident on the interfaces and respectively

Let a ray be incident on making an incident angle

As the ray is travelling from rarer to denser medium; it bends towards the normal

Then it refracts at and bends away from the normal (denser to rarer) forming the emergent ray

This emergent ray forms an angle with the normal at known as the angle of emergence

The angles of refraction are and respectively

Now if the emergent ray is extended backwards to , then we get the angle of deviation, denoted by

tells, to what extent the ray PQ had bent from its original path PQOR to OS, owing to refraction by the prism

Now consider Let,

Now from the diagram, we can write the interior angles as

Similarly

Now simplifying the equation we get

Now let us consider quadrilateral

So, we can say quadrilateral is cyclic

In

From Eqn 1 and 2 we get,

As and

Thus we get a relation between the angle of deviation , the angle of prism , the angle of incidence and the angle of emergence

Revision

The relation between and is also can be written as

The relation relates between the angle of deviation , the angle of prism , the angle of incidence and the angle of emergence

The End