Condition for minimum deviation in a prism
Condition for minimum deviation in a prism :- The angle of deviation of a light ray, while passing through a prism is given by :
Here, cannot be negative and A cannot be zero, hence for deviation(δ) to be minimum, we have,
It means in case of minimum deviation, the angle of incidence(i1) is equal to the angle of emergence(i2).
Let i1 = i2 = i, then applying Snell’s Law at interface AB,
Now applying Snell’s Law at interface AC,
Multiplying equations (1) and (2), we get
Hence in case of minimum deviation, the incident ray PQ passes symmetrically with respect to the refracting faces of the prism and the refracted ray in the prism(QR) is parallel to the base of the prism(BC) as shown in the figure above.
The same condition for minimum deviation in a prism can be derived from the deviation(δ) v/s angle of incidence(i) graph.
From above graph we observe that in case of minimum deviation, i1 = i2.