In a prism, the angle of deviation decreases with increase in the angle of incidence up to a particular angle. This angle of incidence where the angle of deviation in a prism is minimum is called the Minimum Deviation Position of the prism and that very deviation angle is known as the Minimum Angle of Deviation. In Minimum Deviation, the refracted ray in the prism is parallel to its base. In other words, the light ray is symmetrical about the axis of symmetry of the prism. Also, the angles of refractions are equal i.e.. And, the angle of incidence and angle of emergence equal each other. This is clearly visible in the graph in the next section.
The formula for minimum deviation can be derived by exploiting the geometry in the prism. The approach involves replacing the variables in Snell's Law in terms of the Deviation and Prism Angles by making the use of the above properties. From the Angle Sum of, Using the Exterior Angle Theorem in, This can also be derived by putting in the Prism Formula: From Snell's law, This is a convenient way used to measure the refractive index of a material by directing a light ray through a prism of negligible thickness at minimum deviation filled with the material or in a glass prism dipped in it. Ans.: Sol.: Here, , Plugging them in the above formula, Also, This is also apparent in the graph below. Ans.: Sol.: Here, Using the above formula, Also, the variation of the angle of deviation with an arbitrary angle of incidence can be encapsulated into a single equation by expressing in terms of in the Prism Formula using Snell's Law: Finding the minima of this equation will also give the same relation for minimum deviation as above.
For Thin Prism
In a thin or small angle prism, as the angles become very small, the sine of the angle nearly equals the angle itself and this yields many useful results. and are very small, Interestingly, using a similar approach with the Snell's Law and the Prism Formula for an in general thin-prism ends up in the very same result ofr the Deviation Angle. and are small, , and From the Prism Formula, Thus, it can be said that a Thin Prism is always in Minimum Deviation.
Exprimental Determination
Minimum Deviation can be found Manually or with Spectrometer. Either the prism is kept fixed and the incidence angle is adjusted or the prism is rotated keeping the light source fixed.
Minimum Angle of Dispersion
The Minimum Angle of Dispersion for white light is the difference in minimum deviation angle between red and violet rays of a light ray through a prism.
Applications
One of the factors that causes a rainbow is the bunching of light rays at the minimum deviation angle that is close to the rainbow angle. It is also responsible for phenomena like halos and sundogs, produced by the deviation of sunlight in mini prisms of hexagonal ice crystals in the air bending light with a minimum deviation of 22°.
