The formula to calculate the refractive index (μ) of the material of the prism is given by
μ=sin(2A)sin(2A+δm)...(1)
From equation (1), it follows that
cot2A=sin2Asin(2A+δm)
⇒cos2A=sin(2A+δm)⇒sin(2π−2A)=sin(2A+δm)
⇒2A+δm=2π−2A
⇒δm=π−2A