A light ray travels from water to air. If the ray strikes the water/air boundary at an angle of incidence of 46 degrees, what is the angle of refractiob in air? (n water = 1.33)
To find the angle of refraction in air, you can use Snell's law, which states that the ratio of the sines of the angles of incidence and refraction is equal to the ratio of the refractive indices of the media.
Let's denote the angle of incidence as θ1 and the angle of refraction as θ2. The refractive indices of water and air are given as n1 and n2 respectively.
Snell's law can be written as:
n1 * sin(θ1) = n2 * sin(θ2)
In this case, the light ray is traveling from water to air, so n1 = 1.33 (refractive index of water) and n2 = 1 (refractive index of air).
The given angle of incidence is θ1 = 46 degrees. We need to find θ2.
Rearranging the equation above, we get:
sin(θ2) = (n1/n2) * sin(θ1)
Now we can substitute the values:
sin(θ2) = (1.33/1) * sin(46)
Using a calculator, we find:
sin(θ2) ≈ 1.004
However, since the sine of an angle cannot be greater than 1, we can conclude that there is no refracted ray. This phenomenon is known as total internal reflection.
Therefore, the angle of refraction in air is undefined or does not exist.