Name: Waves and Their Phases
Uploaded: 2019-07-19
Duration: 6 min 51 s
Description: In this video, we will learn how two or more waves can be studied in terms of their phases. Equations of two waves and graphs of two waves. Learn more!

Question

What is unpolarised light? Explain with the help of suitable ray diagram how an unpolarised light can be polarised by reflection from a transparent medium. Write the expression for Brewster angle in terms of the refractive index of denser medium.

Accepted Answer

Unpolarized light:

The light having vibrations of electric field vector in all possible directions perpendicular to the direction of wave propagation is called the ordinary (or unpolarized) light.

If unpolarized light falls on a transparent surface of refractive index n at a certain angle $i_{p}$ , called polarising angle, then reflected light is plane polarised with its electric vector perpendicular to the plane of incidence when the refracted and reflected rays make a right angle with each other.

Brewster’s law: $n = i_{p} \tan θ$

In an ordinary or unpolarised ray of light, the vibrations of electric field vector are symmetrically distributed in all the directions but perpendicular to the direction of propagation of the light. Such a ray of light is called a ray of ordinary or unpolarised light.

The arrows represent vibrations in the plane of the paper, while the dots represent vibrations in a direction perpendicular to the plane of the paper.

The simplest method to produce plane polarised light is by reflection.

Therefore, the angle of incidence, at which when ordinary light is incident on transparent refracting medium, the reflected light becomes maximum rich in plane polarised light is called polarising angle. It is denoted by $p$ .

The relation connecting the polarising angle of a medium and its refractive index is given by Brewster's law. It states that when light is incident at polarising angle at the interface of a refracting medium, the refractive index of the medium is equal to the tangent of the polarising angle.
If $p$ is polarising angle and $μ$ , the refractive index of the refracting medium, then according to Brewster's law,
$μ = \tan p . . . . . (i)$
When light is incident at polarising angle, the reflected light is found to be completely plane polarised. When light is incident at polarising angle $p$ on a refracting medium of refractive index $μ$ , let $r$ be the angle of refraction. Then, according to Snell's law,

$μ = \frac{\sin p}{\sin r} . . . . . (i i)$

From the above equations,

$\frac{\sin p}{\sin r} = \tan p = \frac{\sin p}{\cos p}$ or

$\sin r = \cos p$ or

$\sin r = \sin (90 ° - p)$ or

$r = 90 ° - p$ or

$r + p = 90 °$

Hence, when a ray of light is incident at polarising angle, the reflected ray is at right angle to the refracted ray.

What is unpolarised light? Explain with the help of suitable ray diagram how an unpolarised light can be polarised by reflection from a transparent medium. Write the expression for Brewster angle in terms of the refractive index of denser medium.

Important Questions on Wave Optics

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