Refraction problems and total internal reflection

In a problem first draw a diagram, draw the perpendicular and measure the angles from that perpendicular (not from the surface). In reflection problems γ = α and the angle between the incident and reflected rays is 2α; in a plane mirror the image is behind the mirror at the same distance as the object, virtual and the same size. In refraction problems use n₁sin α = n₂sin β: n₂₁ = sin α/sin β, through speeds n₂₁ = v₁/v₂, and relative to vacuum n = c/v. If in the same time light covers s₀ in vacuum and s in a medium, then n = s₀/s, because the path is proportional to the speed. Take sine values from a table or calculator (sin 30° = 0.5; sin 45° ≈ 0.71; sin 60° ≈ 0.87). Check the result: in an optically denser medium we must have β < α.