Find the angle of refraction for light that is incident on a water surface from air when the angle of incident is 40 degrees
To find the angle of refraction for light that is incident on a water surface from air, we can use Snell's law. Snell's law states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the velocities of light in the two mediums:
sin(θᵢ) / sin(θᵣ) = v₁ / v₂
Where:
θᵢ = angle of incidence
θᵣ = angle of refraction
v₁ = velocity of light in medium 1 (air in this case)
v₂ = velocity of light in medium 2 (water in this case)
The velocity of light in a medium is inversely proportional to the refractive index of that medium. The refractive index of air is approximately 1, while the refractive index of water is approximately 1.33.
Let's substitute the values into the equation:
sin(θᵢ) / sin(θᵣ) = 1 / 1.33
Now, we need to solve for θᵣ. Rearranging the equation, we get:
sin(θᵣ) = sin(θᵢ) * 1.33
To find the angle of refraction (θᵣ), we need to take the inverse sine (also known as arcsine) of both sides of the equation:
θᵣ = arcsin(sin(θᵢ) * 1.33)
For the given incident angle of 40 degrees, we can calculate the angle of refraction as follows:
θᵣ = arcsin(sin(40) * 1.33)
Using a calculator, the angle of refraction is approximately 25.26 degrees.