A 45∘–45∘–90∘ glass prism is used as a mirror in binoculars. Light enters perpendicularly to one of the 45∘ faces, but manufacturing tolerances allow the incident rays to deviate by up to 3.0∘ from that normal. Find the minimum refractive index the prism material must have so that every such ray undergoes total internal reflection at the hypotenuse face.