What is Brewster's Law?

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Grade Level:

Class 12

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Definition

What is it?

Brewster's Law tells us that when unpolarized light hits a surface, it becomes completely polarized if the reflected and refracted rays are perpendicular to each other. The angle at which this happens is called the Brewster's angle or polarizing angle.

Simple Example

Quick Example

Imagine light from your mobile screen hitting a shiny floor. If you look at the reflection from a certain angle, the glare (unwanted bright light) might suddenly become much less intense or disappear. This specific angle is related to Brewster's angle, where the reflected light is mostly polarized.

Worked Example

Step-by-Step

Let's find the Brewster's angle for light going from air (refractive index n1 = 1) into water (refractive index n2 = 1.33).

1. Brewster's Law states that tan(ip) = n2 / n1, where ip is the Brewster's angle.
2. Here, n2 (refractive index of water) = 1.33.
3. And n1 (refractive index of air) = 1.
4. So, tan(ip) = 1.33 / 1 = 1.33.
5. To find ip, we take the inverse tangent (tan^-1) of 1.33.
6. ip = tan^-1(1.33) approximately 53.06 degrees.

Answer: The Brewster's angle for light entering water from air is about 53.06 degrees.

Why It Matters

Understanding Brewster's Law is crucial in fields like optics and engineering. It helps in designing polarized sunglasses to reduce glare, or in creating special camera filters. This knowledge is used by engineers making LCD screens and even in laser technology, impacting careers from optical engineers to product designers.

Common Mistakes

MISTAKE: Confusing Brewster's angle with the angle of incidence for total internal reflection. | CORRECTION: Brewster's angle deals with polarization of reflected light, while total internal reflection occurs when light doesn't refract at all, staying within the denser medium.

MISTAKE: Assuming light is always completely polarized at any angle of incidence. | CORRECTION: Light is completely polarized only at the specific Brewster's angle (ip) where reflected and refracted rays are perpendicular.

MISTAKE: Using the wrong refractive indices in the formula (e.g., n1/n2 instead of n2/n1). | CORRECTION: Always remember the formula is tan(ip) = n2 / n1, where n2 is the refractive index of the second medium (where light enters) and n1 is the first medium.

Practice Questions

Try It Yourself

QUESTION: If light travels from air (n=1) into glass (n=1.5), what is the Brewster's angle? | ANSWER: Approximately 56.31 degrees.

QUESTION: For a certain material, the Brewster's angle is 60 degrees when light enters it from air (n=1). What is the refractive index of this material? | ANSWER: Approximately 1.732.

QUESTION: Light is incident on a surface at Brewster's angle. If the refractive index of the first medium is 1.2 and the second medium is 1.8, what is the angle of refraction? (Hint: Remember the relationship between reflected and refracted rays at Brewster's angle). | ANSWER: The angle of refraction is 90 - ip. First, find ip = tan^-1(1.8/1.2) = tan^-1(1.5) approx 56.31 degrees. So, angle of refraction = 90 - 56.31 = 33.69 degrees.

MCQ

Quick Quiz

At Brewster's angle, what is the relationship between the reflected and refracted rays?

They are parallel to each other.

They are perpendicular to each other.

The reflected ray is completely absorbed.

The refracted ray undergoes total internal reflection.

The Correct Answer Is:

Brewster's Law states that at the polarizing angle (Brewster's angle), the reflected and refracted rays are exactly 90 degrees (perpendicular) to each other, leading to complete polarization of the reflected light.

Real World Connection

In the Real World

You experience Brewster's Law every time you wear polarized sunglasses, especially while driving or near water. These glasses are designed to block the horizontally polarized glare (reflected light) from surfaces like wet roads or water bodies, making your vision clearer and safer. This technology is also used in camera lenses to reduce unwanted reflections in photos.

Key Vocabulary

Key Terms

POLARIZATION: The process of restricting the vibrations of light waves to a single plane | REFRACTIVE INDEX: A measure of how much light bends when passing from one medium to another | UNPOLARIZED LIGHT: Light waves vibrating in all possible directions perpendicular to the direction of travel | BREWSTER'S ANGLE: The specific angle of incidence at which reflected light is completely polarized | PERPENDICULAR: At a right angle (90 degrees) to something else.

What's Next

What to Learn Next

Next, explore 'Malus's Law' to understand how the intensity of polarized light changes when it passes through a polarizer. This builds on Brewster's Law by showing how we can control and measure polarized light, which is super useful in many optical devices!