What is the condition for total internal reflection to occur when light travels from a denser medium to a rarer medium?

• A. θ_i = θ_c
• B. θ_i < θ_c
• C. θ_i > θ_c
• D. θ_i ≥ θ_c

Answer: (C)

When light goes from a denser to a rarer medium, Snell’s law sets a limit on refraction: n1 sinθi = n2 sinθt. Since n1 > n2, the largest possible sinθt is 1, which means sinθi cannot exceed n2/n1. The angle θc that satisfies sinθc = n2/n1 is the critical angle. If the incident angle is greater than θc, sinθi > n2/n1, so θt would have to be greater than 90°, which is not possible for a refracted ray; all the light is reflected back into the denser medium. At θi = θc, the refracted ray travels along the boundary (θt = 90°), a limiting case, not full reflection. So the condition for total internal reflection is when the incident angle exceeds the critical angle.