If the glass plate of refractive index is 1.7321 is to be used as a polarized . What would be the 1) polarizing angle 2) angle of retraction Please give me answer

To determine the polarizing angle and the angle of refraction for a glass plate with a refractive index of 1.7321, we can use Brewster's Law and Snell's Law. Let's break down the concepts and calculations step by step.

Understanding Polarizing Angle

The polarizing angle, also known as Brewster's angle, is the angle at which light with a particular polarization is perfectly transmitted through a transparent dielectric surface, with no reflection. Brewster's Law states that this angle can be calculated using the formula:

tan(θp) = n

where θp is the polarizing angle and n is the refractive index of the material. For our glass plate:

Calculating the Polarizing Angle

Given that the refractive index (n) is 1.7321, we can find the polarizing angle as follows:

• Using the formula: tan(θp) = 1.7321
• To find θp, we take the arctangent: θp = arctan(1.7321)

Using a calculator, we find:

θp ≈ 60 degrees

Exploring the Angle of Refraction

Next, we need to find the angle of refraction when light hits the glass plate at the polarizing angle. According to Snell's Law, the relationship between the angles and refractive indices of the two media is given by:

n1 * sin(θ1) = n2 * sin(θ2)

Here, n1 is the refractive index of air (approximately 1), θ1 is the angle of incidence (which is the polarizing angle we just calculated), n2 is the refractive index of the glass (1.7321), and θ2 is the angle of refraction we want to find.

Calculating the Angle of Refraction

Substituting the known values into Snell's Law:

• n1 = 1 (air)
• θ1 = 60 degrees
• n2 = 1.7321 (glass)

We can rearrange Snell's Law to solve for sin(θ2):

sin(θ2) = (n1 * sin(θ1)) / n2

Calculating sin(θ1):

sin(60 degrees) = √3 / 2 ≈ 0.866

Now substituting into the equation:

sin(θ2) = (1 * 0.866) / 1.7321

Calculating this gives:

sin(θ2) ≈ 0.500

Now, to find θ2, we take the arcsine:

θ2 ≈ 30 degrees

Summary of Results

To summarize our findings:

• Polarizing Angle (θp): Approximately 60 degrees
• Angle of Refraction (θ2): Approximately 30 degrees

This analysis shows how the properties of light and materials interact, leading to the fascinating phenomenon of polarization. If you have any further questions or need clarification on any part of this process, feel free to ask!