At minimum deviation, δm=A (angle of minimum deviation equals prism angle). The refractive index formula becomes:
n=sin(2A)sin(2A+δm)=sin(2A)sin(22A)=sin(2A)sinA
Using sinA=2sin(2A)cos(2A):
n=sin(2A)2sin(2A)cos(2A)=2cos(2A)
For a physical prism, 0<A<90°, so 45°<2A<90°, giving 0<cos(2A)<21.
Therefore, 1<n<2⋅2=22. However, more precisely, 2<n<2.