Upward rays of light in water toward the water-air boundary at angles greater than 48 degreees to the normal are totally reflected. No rays beyond 48 degrees refract outside. How about the reverse? Is there an angle at which light rays in air meeting the air-water boundary will totally reflect? Or will some light be refracted at all angles?
Some light is reflected at all angles, for unpolarized light coming from air or vacuum to a higher-index medium such as water. However, for light of a certain linear polarization, there is no reflection at one particular angle angle of incidence, called Brewster's angle.
To understand whether light rays in air meeting the air-water boundary will totally reflect or be refracted at all angles, we need to consider the concept of the critical angle.
The critical angle is the angle of incidence at which light passing from a medium to a more optically dense medium is refracted at an angle of 90 degrees (along the boundary), resulting in total internal reflection. It separates the angles of incidence that lead to refraction from those that result in total internal reflection.
In the case of light traveling from air to water, which is a transition from a less optically dense medium (air) to a more optically dense medium (water), the critical angle can be calculated using Snell's law.
Snell's law states:
n₁sin(θ₁) = n₂sin(θ₂)
where:
- n₁ is the refractive index of the initial medium (air),
- n₂ is the refractive index of the final medium (water),
- θ₁ is the angle of incidence,
- θ₂ is the angle of refraction.
The refractive index of air is approximately 1 and the refractive index of water is around 1.33.
For total internal reflection to occur, the angle of incidence (θ₁) must be greater than or equal to the critical angle (θc). When the angle of incidence exceeds the critical angle, all the light is reflected back into the first medium rather than being refracted into the second medium.
To calculate the critical angle for the air-water boundary, we can rearrange Snell's law:
sin(θc) = n₂ / n₁
Using the refractive indices for air and water:
sin(θc) = 1.33 / 1 = 1.33
Since the sine function is limited to values between -1 and 1, it is not possible for sin(θc) to exceed 1. Therefore, there is no angle of incidence at which light rays in air meeting the air-water boundary will totally reflect.
At all angles of incidence, some light will be refracted into the water. The amount of refraction will vary depending on the angle of incidence.
It's worth noting that only when the angle of incidence is greater than the critical angle will total internal reflection occur, resulting in no light being refracted into the water.