For light going from water to air, what is the critical angle in water for total internal reflection?

For light going from water to air, what is the critical angle in water for total internal reflection?

• A. 40°
• B. 48.6°
• C. 60°
• D. 30°

Answer: (B)

Light moving from a denser medium to a rarer medium can undergo total internal reflection once the angle of incidence exceeds a certain critical angle. That angle comes from sin theta_c = n2 / n1, where n1 is the refractive index of water and n2 is that of air. Using n1 ≈ 1.33 and n2 ≈ 1.00, sin theta_c ≈ 1.00 / 1.33 ≈ 0.752. Taking the arcsin gives theta_c ≈ 48.8 degrees, so about 48.6 degrees is the right value. Beyond this angle, light cannot refract into air and is completely reflected back into water. The other options don’t fit because they would require different index ratios than water to air.

Light moving from a denser medium to a rarer medium can undergo total internal reflection once the angle of incidence exceeds a certain critical angle. That angle comes from sin theta_c = n2 / n1, where n1 is the refractive index of water and n2 is that of air. Using n1 ≈ 1.33 and n2 ≈ 1.00, sin theta_c ≈ 1.00 / 1.33 ≈ 0.752. Taking the arcsin gives theta_c ≈ 48.8 degrees, so about 48.6 degrees is the right value. Beyond this angle, light cannot refract into air and is completely reflected back into water. The other options don’t fit because they would require different index ratios than water to air.