Prism formula | Derivation of prism formula
Prism formula | Derivation of prism formula :- As we have seen in article Condition for minimum deviation in a prism, in case of minimum deviation,
i1 = i2 = i (let) and
r1 = r2 = r (let)
Now as , so in case of minimum deviation,
Also , in case of minimum deviation,
Using Snell’s Law,
This is called prism formula. It is used for accurate determination of refractive index of a transparent medium, of which the prism is made.
A ray of light falling at an angle of 50° is refracted through a prism and suffers minimum deviation. The angle of the prism is 60° . Find the angle of minimum deviation and refractive index of the material of the prism.
Here i1 = 50°, A = 60°, δm = ? and μ = ?
In case of minimum deviation, i1 = i2 = i = 50°
Using δm = 2i – A
⇒ δm = 2(50°) – 60° = 40°
Now using , we get
For a glass prism μ=√3 the angle of minimum deviation is equal to the angle of the prism. Find the angle of the prism.
Here it is given that δmin = A
Using , and putting δmin = A, we get