Light in air strikes a water surface at the polarizing...

Light in air strikes a water surface at the polarizing angle. The part of the beam refracted into the water strikes a submerged slab of material with refractive index $n=1.62$ as shown in Figure P 38.59. The light reflected from the upper surface of the slab is completely polarized. Find the angle $\theta$ between the water surface and the surface of the slab.

Key Concepts

Brewster's Angle

Brewster's angle is the angle of incidence at which light reflected off a surface is completely polarized. At this particular angle, the reflected and refracted rays are perpendicular to each other. This concept is essential in understanding how specific orientations between different media yield fully polarized reflected light, and it helps in designing systems that utilize polarized light for various optical applications.

Snell's Law

Snell's law describes how light bends when it passes from one medium into another with a different refractive index. It relates the sine of the angle of incidence to the sine of the angle of refraction by the ratio of the refractive indices of the two media. This principle is fundamental in analyzing and predicting the path of light at interfaces, which is critical when determining the angles involved in multi-layer optical systems.

Refractive Index

The refractive index is a measure of how much a medium slows down light relative to its speed in a vacuum. It determines the degree to which light bends when entering or exiting the medium. Understanding refractive indices is crucial for calculating Brewster's angle and applying Snell's law, as these values directly affect the light's trajectory and polarization characteristics at interfaces.

Polarization by Reflection

Polarization by reflection refers to the phenomenon where light becomes partially or completely polarized after reflecting from a surface, particularly at certain angles such as Brewster's angle. This concept explains the conditions under which the reflected light has its electric field vectors oriented in a specific direction, and it is vital for understanding and manipulating light in optical devices and experiments.

Transcript

00:01 So in this problem, i'm referring to the figure p38 .39 from the text, and i just redraw the answer figure to this one here.

00:12 The light in the air first strikes water surface at the polarizing angle.

00:19 Now, the part of the beam that is refracted into the water strikes a slab of refractive index 1 .62 at the polarizing angle again.

00:28 There are like two different polarizing angles, one corresponding to the polarizing angle at the water surface, the other one at the slab surface.

00:37 Those are the two different angles anywhere.

00:40 Now, we want to find the angle data between the water surface and the slab surface.

00:45 So the angle data is shown in the figure over here.

00:48 Okay.

00:48 So that's what we want to find out.

00:50 Now, first of all, since the polarizing, since the incident angle is at polarizing angle on the one, water surface, the angle, the reflected beam is going to reflect, reflected ray is going to make the 90 degree angle with the refracted ray.

01:11 Okay, that's the condition for the polarizing as well, polarization as well.

01:15 So this over here is going to be 90 degrees.

01:19 So that means theta p plus theta 2 has to be 90 degrees as well because this is the straight line and the sum has to be 180 degrees, right? so that means theta 2 plus theta p equals 90 degrees.

01:42 Also in the triangle, in this triangle over here, i'm just going to circle in this triangle over here, this small triangle over here.

01:53 You can see that theta plus 90 plus theta 2 plus plus.

02:03 90 minus theta p prime equals 180 degrees.

02:11 I'm going to explain this to you how this is true.

02:15 So this is theta here.

02:18 So that means, so this is theta...

Please give Ace some feedback