For an equilateral prism, the angle of the prism is A=60∘.
Given that the angle of minimum deviation is half of the angle of the prism:
δm=2A=260∘=30∘
The refractive index of the prism is given by:
μ=sin(2A)sin(2A+δm)
Substituting the values of A and δm:
μ=sin(260∘)sin(260∘+30∘)
μ=sin(30∘)sin(45∘)
μ=2121=2
Answer: 2