A light wave strikes a lake at an angle of incidence of 65.4 degrees. At what angle of refraction will this wave travel through the lake? (The index of refraction of water is 1.33 and the index of refraction of air is 1.00)
If you are measuring the angles from the surface normal, then it will be bent towards the normal.
1*sin65.4=1.33sinT
sinT=3/4 * sin(65degrees)
T=arcsin( )=42.8 degrees
To find the angle of refraction, we can use Snell's law, which relates the angles of incidence and refraction to the indices of refraction of the two media.
Snell's law states that the ratio of the sines of the angles of incidence and refraction is equal to the ratio of the indices of refraction:
n1 * sin(θ1) = n2 * sin(θ2)
where:
n1 is the index of refraction of the initial medium (air),
θ1 is the angle of incidence,
n2 is the index of refraction of the second medium (water), and
θ2 is the angle of refraction (what we are trying to find).
In this case, n1 = 1.00 (index of refraction of air) and n2 = 1.33 (index of refraction of water), and θ1 = 65.4 degrees.
Rearranging Snell's law, we can solve for θ2:
sin(θ2) = (n1 / n2) * sin(θ1)
Plugging in the values, we get:
sin(θ2) = (1.00 / 1.33) * sin(65.4)
Now, we can calculate θ2 by taking the inverse sine (arcsine) of both sides:
θ2 = arcsin((1.00 / 1.33) * sin(65.4))
Using a calculator, we find that θ2 is approximately 48.1 degrees.
Therefore, when the light wave travels through the lake, it will be refracted at an angle of approximately 48.1 degrees.