using Snell's Law (sin(theta1)/sin(theta2) = v1/v2 where (theta1) is the angle of incidence and (theta2) is the angle of refration. The number V1/V2 is called the index of refraction. The index of refraction from air to water is 4/3. If a ray of light passes through the surface of a lake at an angle of incidence of 70 degrees what is the angle of refraction?
To find the angle of refraction using Snell's law, you need to know the indices of refraction for the two media involved. In this case, the index of refraction from air to water is given as 4/3.
The formula you mentioned is sin(theta1) / sin(theta2) = v1 / v2.
In this case, theta1 represents the angle of incidence and theta2 represents the angle of refraction. v1 and v2 represent the indices of refraction for the respective media.
Now, let's plug in the given values:
Given: theta1 = 70 degrees
Index of refraction from air to water = v1/v2 = 4/3
Using Snell's law, we can rewrite the equation as:
sin(theta1) / sin(theta2) = v1 / v2
Plugging in the values:
sin(70) / sin(theta2) = 4/3
To find the angle of refraction (theta2), we need to isolate sin(theta2) on one side of the equation. We can do this by cross-multiplying:
3 * sin(70) = 4 * sin(theta2)
Now, divide both sides by 4:
(3 * sin(70)) / 4 = sin(theta2)
Calculate the value on the left side of the equation:
(3 * 0.9397) / 4 = sin(theta2)
2.8191 / 4 = sin(theta2)
0.7048 = sin(theta2)
To find the angle of refraction (theta2), we need to take the inverse sine (arcsine) of 0.7048. In other words:
theta2 = arcsin(0.7048)
Using a scientific calculator or a trigonometric table, we find:
theta2 ≈ 44.47 degrees
Therefore, the angle of refraction is approximately 44.47 degrees.