A light ray in water is directed at the water surface at an angle of incidence at 40 degrees. Calculate the angle of refraction of the light ray at this surface.
To calculate the angle of refraction of a light ray at a water surface, 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 indices of refraction of the two mediums.
The index of refraction of air is approximately 1, while the index of refraction of water is approximately 1.33.
Let's use Snell's Law to calculate the angle of refraction:
sin(angle of incidence) / sin(angle of refraction) = index of refraction of air / index of refraction of water
sin(40 degrees) / sin(angle of refraction) = 1 / 1.33
To calculate the angle of refraction, we can rearrange the equation as:
sin(angle of refraction) = sin(40 degrees) * (index of refraction of water / index of refraction of air)
sin(angle of refraction) = sin(40 degrees) * (1.33 / 1)
sin(angle of refraction) = 0.6428 * 1.33
sin(angle of refraction) = 0.8564
To find the angle of refraction, we take the inverse sine of the value, which is approximately:
angle of refraction ≈ arcsin(0.8564)
angle of refraction ≈ 59.2 degrees
Therefore, the angle of refraction of the light ray at the water surface is approximately 59.2 degrees.
To calculate the angle of refraction, we can use Snell's Law. Snell's Law relates the angle of incidence and the angle of refraction of a light ray as it passes through the interface between two different media.
Snell's Law states:
n₁ * sin(θ₁) = n₂ * sin(θ₂)
Where:
n₁ = refractive index of the medium in which the incident ray is traveling (in this case, water)
θ₁ = angle of incidence
n₂ = refractive index of the medium in which the refracted ray is traveling (in this case, also water, but since we are calculating the angle of refraction within the same medium, it will be 1)
θ₂ = angle of refraction (what we are trying to find)
Given:
θ₁ = 40 degrees
n₁ (refractive index of water) = 1.33
n₂ (refractive index of water) = 1
Now let's substitute the given values into Snell's Law and solve for θ₂:
1.33 * sin(40) = 1 * sin(θ₂)
sin(θ₂) = (1.33 * sin(40))/1
sin(θ₂) = 0.8394
To find θ₂, we need to take the inverse sine (sin⁻¹) of 0.8394:
θ₂ = sin⁻¹(0.8394)
Using a scientific calculator, you can find that θ₂ is approximately 57.13 degrees.
Therefore, the angle of refraction of the light ray at the water surface is approximately 57.13 degrees.