Polarization Formula

Polarization is defined as a phenomenon generated by the wave nature of electromagnetic radiation. Polarized light is a state in which the light waves are parallel to one other. It is possible to polarise only transverse waves as light is made up of them. The amount of polarization depends entirely on the substance and the angle at which the light is reflected. To put it another way, it depends on the refractive index of the material. It is categorized into three types, linear polarization, circular polarization, and elliptical polarization.

Polarization Formula 

The degree of polarization for material or substance is expressed by a polarizing angle, also known as Brewster’s angle. Its formula is equal to the tangent inverse of the ratio of refractive indices of the final and initial media, respectively. It is a unitless quantity ad and hence has no dimensional formula. It is denoted by the symbol θ.

tan θ = n₂/n₁

Where,

n₁ is the refractive index of initial media through which the light propagates,

n₂ is the refractive index of final media which reflects light.

Sample problems

Problem 1: Calculate the polarization angle if the refractive index of initial and final media are 1.562 and 1.345.

Solution:

We have,

n₁ = 1.562

n₂ = 1.345

Using the formula we have,

tan θ = n₂/n₁

tan θ = 1.345/1.562

tan θ = 0.86

θ = 40.73°

Problem 2: Calculate the polarization angle if the refractive index of initial and final media are 1.671 and 1.261.

Solution:

We have,

n₁ = 1.671

n₂ = 1.261

Using the formula we have,

tan θ = n₂/n₁

tan θ = 1.261/1.671

tan θ = 0.75

θ = 37.04°

Problem 3: Calculate the polarization angle if the refractive index of initial and final media are 2 and 1.5.

Solution:

We have,

n₁ = 2

n₂ = 1.5

Using the formula we have,

tan θ = n₂/n₁

tan θ = 1.5/2

tan θ = 0.75

θ = 37.04°

Problem 4: Calculate the refractive index of the initial media if the polarization angle is 50° and the final media index is 1.3.

Solution:

We have,

θ = 50°

n₂ = 1.3

Using the formula we have,

tan θ = n₂/n₁

n₁ = n₂/tan θ

= 1.3/tan 50°

= 1.0908

Problem 5: Calculate the refractive index of the initial media if the polarization angle is 27° and the final media index is 2.6.

Solution:

We have,

θ = 27°

n₂ = 2.6

Using the formula we have,

tan θ = n₂/n₁

n₁ = n₂/tan θ

= 2.6/tan 27°

= 5.103

Problem 6: Calculate the refractive index of the final media if the polarization angle is 56° and the initial media index is 1.2.

Solution:

We have,

θ = 56°

n₁ = 1.2

Using the formula we have,

tan θ = n₂/n₁

n₂ = n₁ tan θ

= 1.2 tan 56°

= 1.779

Problem 7: Calculate the refractive index of the final media if the polarization angle is 32° and the initial media index is 1.8.

Solution:

We have,

θ = 32°

n₁ = 1.8

Using the formula we have,

tan θ = n₂/n₁

n₂ = n₁ tan θ

= 1.8 tan 32°

= 1.125