# Derive the expression for refractive index of the material of the prism in terms of angle of the prism and angle of minimum deviation.

#### In the given diagram,OP is the incidence ray, which is making the angle i1 with normal, and QR is the angle of emergence, which is represented by i2. A is the prism angle and μ is the refractive index of the prism.

Now, We know that,

A=Prism angle, δ=Angle of deviation, i1=Angle of incidence, i2=Angle of emergent.

In the case of minimum deviation,∠r1=∠r2=∠r

A=∠r1+∠r2

SO, A=∠r+∠r=∠2r

∠r=A2

Now, again

A+δ=i1+i2 (∵ In the case of minimum deviation

i1=i2=i and δ=δm)

So, A+δm=i+i=2i

Now, i=A+δm2

Now, from snell's rule,

μ=sin isin r

μ=sinA+δm2sinA2