What is the critical angle for total internal reflection at a water-to-air interface? (n_water ≈ 1.33, n_air ≈ 1.00)

What is the critical angle for total internal reflection at a water-to-air interface? (n_water ≈ 1.33, n_air ≈ 1.00)

• A. About 30.0°
• B. About 45.0°
• C. About 60.0°
• D. About 48.6°

Answer: (D)

When light moves from a denser medium to a rarer one, there’s a maximum incident angle at which it can refract; beyond that, it is totally internally reflected. This critical angle occurs when the refracted ray runs along the boundary, so the angle of refraction is 90°. The relationship is sin(theta_c) = n2 / n1, where n1 is the starting medium and n2 is the destination. For water to air, n1 ≈ 1.33 and n2 ≈ 1.00. So sin(theta_c) ≈ 1.00 / 1.33 ≈ 0.752. Taking the arcsin gives theta_c ≈ 48.6 degrees. Hence the critical angle is about 48.6 degrees. The other values don’t fit because they correspond to sin values of 0.5, 0.707, or 0.866, which would require n2/n1 equal to those numbers, not 1/1.33.

When light moves from a denser medium to a rarer one, there’s a maximum incident angle at which it can refract; beyond that, it is totally internally reflected. This critical angle occurs when the refracted ray runs along the boundary, so the angle of refraction is 90°. The relationship is sin(theta_c) = n2 / n1, where n1 is the starting medium and n2 is the destination.

For water to air, n1 ≈ 1.33 and n2 ≈ 1.00. So sin(theta_c) ≈ 1.00 / 1.33 ≈ 0.752. Taking the arcsin gives theta_c ≈ 48.6 degrees. Hence the critical angle is about 48.6 degrees.

The other values don’t fit because they correspond to sin values of 0.5, 0.707, or 0.866, which would require n2/n1 equal to those numbers, not 1/1.33.