Why is there only one minimum deviation point for a prism?

[Dearth Vader]

I'm having an issue in comprehending the minimum deviation offered by a prism. The fact that we could use the symmetry argument about the angle of incidence and angle of emergence being equal for minimum deviation make sense to me but I couldn't understand why we can be so sure of exactly 1 such point.

I obtained an explicit function of the deviation(any) in terms of the angle of incidence alone but I can't analyse it with my current knowledge of inverse functions. I'm in class 12.


Thank You.

 

[member 553083]

The reason why there is only one minimum deviation point for a prism is because of the way light refracts when passing through the prism. When light passes through the prism, it is bent according to Snell's Law which states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the indexes of refraction of the two materials. Since the index of refraction of the prism is constant, the angle of refraction will vary depending on the angle of incidence and thus, the amount of refraction. As the angle of incidence increases, the angle of refraction also increases, resulting in an increasing amount of refraction. When the angle of incidence reaches a certain point, the angle of refraction will reach a maximum, resulting in a minimum deviation point. This point is unique for each prism and is the point at which the minimum deviation occurs.