Brewsters Law

If you have ever been hiking, you must have taken polarized sunglasses with you as well. Thus, when the weather is sunny, you can’t help but notice the crystal clear reflection that is on a lake. These reflections are polarized. However, when you see it through your sunglasses, you will notice these reflections are gone. Well, it happens because your sunglasses are polarized. They enable only polarized light to go through them. Moreover, polarizers are also present in monitors and TV screens as well to reduce glare. Learn brewsters law here.

Definition

As you all know, the reflected light is polarized but all of it isn’t. When it is in the plane of a reflection, it makes light polarized at 90 degrees to that plane. That is more likely to reflect. Actually, when you shine your light at any particular angle, it creates a huge impact on how polarized the reflection is going to be. Thus, Brewster’s Law is there to assist us in describing how it varies with angle.

As per the Brewster’s Law, the maximum polarization takes place when the angle is 90 degrees in between the reflected ray and refracted ray. This law was named after the famous Scottish Physicist, Sir David Brewster. It was proposed in the year 1811. Furthermore, even the polarization angle is Brewster’s angle.

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Brewsters Law

As the Brewster’s Law states that we can achieve the maximum polarization of light by allowing the ray to fall on a transparent medium’s surface so that the refracted ray becomes perpendicular to the reflected ray. It develops a relationship between the polarizing angle ip and the refractive index. It states that the tangent of the polarizing angle is numerically equal to the refractive index of the medium.

A polarizing angle forms when at a certain angle of incidence, the reflected light is entirely polarized and this specific value of the angle of incidence is recognized as the polarizing angle. The polarizing angle ip hinges on the refractive index mu of the transparent material.

We express the relation as \(\mu\) = tan ip

Over here:

\(\mu\) refers to the refractive index of the transparent medium

ip is the polarizing angle of incidence (p is in subscript) = Brewster angle

When unpolarized light is incident on a transparent medium at any polarizing angle then the rays which transfer and reflect are vertical to each other.

Further, we see that as \(\mu\ = \frac{(sin ip)}{(sin r)}\)

Therefore, tan ip = \(\frac{(sin ip)}{(sin r)}\)

Solved Examples 

Question- If the refractive index of a polarizer is 1.9218. What will be the polarization angle and angle of refraction?

Answer- Looking at the above figures, we will see that we already know the refractive index of the polarizer, that means μ is 1.9218. In order to find the polarization angle and angle of refraction, we will apply Brewster’s law:

μ = tan ip

Or, ip = tan−1tan−1 (1.9128)

Or, ip = 62o 24’

Now we will see that our angle of refraction:

It is specified that ip + ir = 90 degrees

Thus, angle of refraction or ir = 90 – 62o 24’

Therefore, our angle of refraction comes as 27.6 o

Question- Find out Brewster’s angle of light which travels from water (n = 1.33) into the air?

Answer- Looking at the question, we see we have already got our \(n_{1}\) as 1.33. Thus, by applying the formula we will get:

Brewster’s angle = \(tan^{-1} \left (\frac{n^{2}}{n^{1}}\right )\)

Brewster’s angle = \(tan^{-1} \left (\frac{1.5}{1.33}\right )\)

So, Brewster’s angle = 48.4°

Therefore, the brewster’s angle is 48.4°.