To find the critical angle for total reflection at the water-air interface, we can use Snell's law, which relates the angle of incidence (θi) to the angle of refraction (θr) when light passes from one medium to another:
n1 * sin(θi) = n2 * sin(θr)
Here, n1 is the refractive index of the first medium (water in this case) and n2 is the refractive index of the second medium (air).
Given: n1 = 1.33 (refractive index of water) n2 = 1 (refractive index of air)
We need to find the critical angle, which occurs when the angle of refraction is 90 degrees. Therefore, sin(θr) = 1.
Plugging the given values into Snell's law, we have:
1.33 * sin(θi) = 1 * 1
Simplifying the equation:
sin(θi) = 1 / 1.33 θi = arcsin(1 / 1.33)
Using a calculator, we can find the inverse sine of 1/1.33:
θi ≈ 48.75 degrees
So, the critical angle for total reflection at the water-air interface is approximately 48.75 degrees.