For water n(red)= 2.332 and n(blue)=1.340. What are the underwater angles of refraction for the red and blue components of a white light beam in air incident at an angle of 82 on a water surface?
To find the underwater angles of refraction for the red and blue components of a white light beam, we can use Snell's law, which relates the angles of incidence and refraction to the refractive indices of the materials involved.
Snell's law can be written as:
n1 * sin(theta1) = n2 * sin(theta2)
Where:
- n1 and n2 are the refractive indices of the incident and refracted media, respectively.
- theta1 is the angle of incidence.
- theta2 is the angle of refraction.
In this case, the incident medium is air, and the refracted medium is water.
Given:
- n(red) = 2.332 (refractive index for red light in water)
- n(blue) = 1.340 (refractive index for blue light in water)
- theta1 = 82° (angle of incidence in air)
First, let's calculate the angle of refraction for the red component:
Using Snell's law, we can rearrange the equation to solve for theta2:
theta2 = arcsin((n1 * sin(theta1)) / n2)
Substituting the values:
theta2(red) = arcsin((1 * sin(82°)) / 2.332)
Using a scientific calculator, we find that theta2(red) ≈ 36.78°
Now, let's calculate the angle of refraction for the blue component:
Using Snell's law and substituting the values:
theta2(blue) = arcsin((1 * sin(82°)) / 1.340)
Using a scientific calculator, we find that theta2(blue) ≈ 57.40°
So, the underwater angles of refraction for the red and blue components of the white light beam are approximately 36.78° and 57.40°, respectively.