A beam of light is incident on a flat piece of polystyrene at an angle of 55 degrees relative to a surface normal. What angle does the refracted ray make with the plane of surface?
thank you
Use Snell's law.
To find the angle the refracted ray makes with the plane of the surface, we can use Snell's law, which relates the angles of incidence and refraction to the refractive indices of the two mediums involved.
Snell's law states that the ratio of the sines of the angles of incidence (θ1) and refraction (θ2) is equal to the ratio of the refractive indices (n1 and n2) of the two mediums. Mathematically, it can be represented as:
n1 * sin(θ1) = n2 * sin(θ2)
Given that the incident angle (θ1) is 55 degrees and the medium is polystyrene, which has a refractive index of approximately 1.59 (n1), we can substitute these values into the equation.
1.59 * sin(55) = n2 * sin(θ2)
Now, to find the angle of refraction (θ2), we rearrange the equation:
sin(θ2) = (1.59 * sin(55)) / n2
Next, we need to determine the refractive index (n2) of the medium the light is entering. If it's entering another piece of polystyrene, we can assume the refractive index is the same (n2 = 1.59). If it's entering a different material, you would need to know the refractive index of that material.
For the sake of explanation, let's assume the light is entering another piece of polystyrene. Substituting n2 = 1.59 into the equation, we have:
sin(θ2) = (1.59 * sin(55)) / 1.59
Now, we can calculate the value of sin(θ2) using a calculator:
sin(θ2) ≈ 0.872
Finally, to find the angle of refraction (θ2), we take the inverse sine (or arcsine) of 0.872:
θ2 ≈ arcsin(0.872)
Using a calculator, we find:
θ2 ≈ 60.47 degrees
Therefore, the refracted ray makes an angle of approximately 60.47 degrees with the plane of the surface.