We know that a prism is an optical equipment which changes the direction of light that falls on it.
The image shows a ray of white light incident on a prism that undergoes deviation (change of direction).
The extent of deviation depends on factors that are related to the prism and the light itself.
Before discussing the factors affecting the angle of deviation, let us introduce an equation first.
The mathematical relation between the angle of incidence i1, the angle of emergence i2, the angle of the prism A and the angle of deviation δ is i1+i2=A+δ
Now, we will list down all the factors that affect the angle of deviation and briefly explore each one of them.
Let's begin with the first factor.
1. Angle of deviation, δ, is dependent on the angle of incidence, i1.
Experimental observation tells that if we increase i1, the corresponding δ will first decrease until it attains a minimum value δm. Further increasing i1 will increase δ.
The graph between δ and i1 is plotted above. The value of i1 for which δ→δm is labeled .
The situation δ→δm occurs when →i1=i2, i.e. the angle of incidence and the angle of emergence are equal, or, →r1=r2 i.e. the angles of refraction are equal.
If i1=i2=i, then equation i1+i2=A+δ, gives δm=2i−A∵δ→δmwheni1=i2
It is interesting to note that this particular value of δm is unique for a particular glass prism and a particular colour of light.
This is because, for different colours, the angle of incidence i1 corresponding to δm will be different.
So different i1 will consequently give different δm.
Let us look at the second factor now.
2. In addition to the angle of incidence, the angle of deviation, δ, also depends on the refractive index, μ, of the medium.
The dependence of δ on μ is linear as δ∝μ This means, denser the medium, greater will be the angle of deviation and vice versa.
Let us look at the third factor.
3. δ is also dependent on the angle of the prism A i.e. δ∝A
This simply means that if the angle of the prism is large, the angle of deviation is large too and vice versa.
Finally, let us look at the fourth factor.
4. Lastly, δ also depends on the wavelength of the light (λ) used and is inversely proportional to the wavelength, i.e.δ∝λ1
This means, more the value of the wavelength, less will be the angle of deviation and vice versa.
If we compare red and violet colours, λred>λviolet consequently, δviolet>δred
So, violet deviates the most and red deviates the least. Other colours are in the intermediate positions.
Revision
The angle of deviation depends on the angle of incidence and the relation between them is described by this curve.
When the angle of incidence and emergence are the same we get a minimum deviation given by
δm=2i−A
Angle of deviation, δ, is dependent on the angle of incidence, i1.
The angle of deviation, δ, also depends on the refractive index, μ, of the medium.
δ is dependent on the angle of the prism A.
Lastly, δ also depends on the wavelength of the light(λ) used and is inversely proportional to it.