Given an equilateral prism, the angle of the prism is A=60∘.
The refractive index of the prism is μ=2.
The emergent ray grazes the second surface, which means the angle of emergence is e=90∘.
Applying Snell's law at the second surface: μsin(r2)=1⋅sin(e).
2sin(r2)=sin(90∘)=1.
sin(r2)=21, which gives r2=45∘.
For a prism, we know the relation r1+r2=A.
Substituting the values: r1+45∘=60∘.
r1=60∘−45∘=15∘.
The angle of refraction at the incident surface is r1=15∘.