Light travelling in water is incident on air refracts at an angle of 27 degrees. What is the angle of incidence?
my answer: 37 degrees
To find the angle of incidence, we can use Snell's law, which relates the angle of incidence to the angle of refraction and the refractive indices of the two media. In this case, light is traveling from water to air.
Snell's law states:
n1 * sin(angle1) = n2 * sin(angle2)
where:
n1 and n2 are the refractive indices of the first and second media respectively, and
angle1 and angle2 are the angles of incidence and refraction.
Given that the angle of refraction is 27 degrees and the first medium is water, we can find its refractive index. The refractive index of water is approximately 1.33.
Plugging in the values into Snell's law:
1.33 * sin(angle1) = 1 * sin(27)
We want to find angle1, the angle of incidence. Rearranging the equation:
sin(angle1) = sin(27) / 1.33
Now, we can solve for angle1 by taking the inverse sine of both sides:
angle1 = arcsin(sin(27) / 1.33)
Using a calculator, we can find:
angle1 ≈ 20.6 degrees.
Therefore, the angle of incidence is approximately 20.6 degrees.
To find the angle of incidence in this situation, you can use Snell's Law, which 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 media. In this case, the light is traveling from water to air.
So, let's assign some variables:
- Angle of incidence: θ1
- Angle of refraction: θ2
- Velocity of light in water: v1
- Velocity of light in air: v2
Snell's Law can be written as:
sin(θ1) / sin(θ2) = v1 / v2
To find θ1, we need to rearrange the equation. First, let's substitute the known values:
sin(27°) / sin(θ2) = v1 / v2
Now, we can solve for sin(θ2) by isolating it on one side of the equation:
sin(θ2) = (v2 * sin(27°)) / v1
Finally, to find θ2, take the inverse sine (sin^-1) of both sides:
θ2 = sin^-1((v2 * sin(27°)) / v1)
However, without knowing the specific values for the velocities of light in water and air, we cannot calculate the exact angle of incidence in this case.