# Angle of refraction at minimum deviation of two different colours

I was thinking, if two separate light beams of red and violet colour are passed separately through an equilateral prism, such that the angle of deviation is minimum in both cases, will the angle of refraction inside the prism just simply be 30 degrees (from relation: A=2r) in both cases, or do we have to consider the fact that one beam is of red colour and the other beam is of blue colour, (which have different angles of refraction in a non-minimum deviation case) ?

So basically my question is that: Does colour(wavelength) of light have an effect on angle of refraction, when we are specifically considering the case of minimum deviation through an equilateral prism?

Yes, angle of refraction would be same for both the lights but their deviation would not be equal.

Let's work out for a thin prism(as we can do calculation for it!)

The angle of deviation is given by $$δ=(n-1)A$$ Where n is the refractive index of the prsim and A is the angle of the prism.

The refractive index of a material depends upon the wavelength of the light(it is an inverse relation). Hence n will be greater for voilet, as a result of which it will suffer greater deviation than red light( see dispersion of light by a prism).

Now the point to be noted here is that the angle of incidence will not be equal for both the lights to have minimum deviation in each of them(calculation done below). From Snell's Law $$n_1\sin i=n_2\sin r$$ Assuming $n_1=1$ and $n_2=n$ and angle of incidence to be small(in order to get a clear picture) $$i=nr$$ Also $$r=\frac{A}{2}$$ $$i=n\frac{A}{2}$$ As mentioned above n will be greater for voilet light and Hence it's angle of incidence (for minimum deviation) will be greater.

• So given that the incident ray is a white light, then only one color will be in the state of minimum derivation, right?
– Jack
Jan 8 at 6:23

When we consider the case of minimum deviation we are assuming $\theta1=\theta2=\theta$ and $\theta1'=\theta2'=\theta'$. So deviation suffered by all the colours is the same. Also the value of R.I.($n$) is of yellow color for this case.

So we find that angle of prism doesn't get affected the color of light at minimum deviation. Hope that helped.

• This is only in case of min deviation, am I right?
– devb
Apr 20, 2017 at 13:01
• Yes, you can check that using geometry. Also the maths support this. Apr 20, 2017 at 13:07
• Thank you sir : ) I would have up upvoted your answer but my rep is too less :p
– devb
Apr 20, 2017 at 13:08

The index of refraction (ratio of speed of light in vacuum to that in the material) depends on the wavelength of light. The angle of refraction depends on refractive index, so it also depends on the wavelength of light.

The deviation of light through a prism depends on refraction, therefore it also depends on the wavelength of light. This is true whether the deviation is minimum or not.

For minimum deviation, the angle of deviation will be different for red and blue light. This angle depends on the refractive index of the prism material as well as the apex angle of the prism. Even though the apex angle is the same (it is the same prism), the refractive index is different.