Sunlight strikes a fused quartz surface. At what angle of incidence is the reflected light completely polarized?
The index of refraction of fused quartz is N = 1.485
You want the "Brewster" angle of indidence.
It is tan^-1(N) = 55.6 degrees
To determine the angle at which the reflected light is completely polarized from a fused quartz surface, we need to consider the optical properties of the material.
First, it is important to note that when light reflects off a surface, it can become polarized, meaning the light waves vibrate in a specific direction. In the case of fused quartz, reflection at a specific angle can achieve complete polarization.
The angle at which the reflected light becomes completely polarized is called the Brewster's angle. At this angle, the reflected light waves are purely polarized perpendicular to the plane of incidence, meaning they vibrate parallel to the surface.
To calculate Brewster's angle, we can use Snell's law, which relates the angles and indices of refraction of light passing through different media.
The refractive index of fused quartz is approximately 1.46. Snell's law states the following equation:
n₁sin(θ₁) = n₂sin(θ₂)
Where:
n₁ = refractive index of the first medium (air/vacuum = 1 in this case),
θ₁ = angle of incidence,
n₂ = refractive index of the second medium (fused quartz = 1.46 in this case),
θ₂ = angle of refraction (which will be 90 degrees at Brewster's angle).
Rearranging the equation, we can solve for θ₁:
θ₁ = arcsin(n₂/n₁)
Plugging in the appropriate values, we get:
θ₁ = arcsin(1.46/1) ≈ 61.57 degrees
Therefore, at an angle of approximately 61.57 degrees of incidence, the reflected light from a fused quartz surface is completely polarized.