What is Malus's Law?

S7-SA4-0105

Grade Level:

Class 12

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Definition

What is it?

Malus's Law describes how the intensity of light changes after passing through a polariser. It states that the intensity of polarised light transmitted through a second polariser (called the analyser) is directly proportional to the square of the cosine of the angle between the transmission axes of the two polarisers.

Simple Example

Quick Example

Imagine you have special sunglasses that block certain light waves. If you hold two such sunglasses one behind the other, and rotate one of them, the amount of light you see coming through will change. When their blocking directions are aligned, you see maximum light. When they are perpendicular, you see minimum (or no) light.

Worked Example

Step-by-Step

Let's say a beam of polarised light with an initial intensity of 100 units passes through an analyser. The angle between the transmission axis of the polarised light and the analyser is 30 degrees.

Step 1: Identify the initial intensity (I_0) = 100 units.
---Step 2: Identify the angle (theta) = 30 degrees.
---Step 3: Recall Malus's Law: I = I_0 * cos^2(theta).
---Step 4: Calculate cos(30 degrees). cos(30) is approximately 0.866.
---Step 5: Calculate cos^2(30 degrees). (0.866)^2 is approximately 0.75.
---Step 6: Multiply the initial intensity by this value. I = 100 * 0.75.
---Step 7: Calculate the final intensity. I = 75 units.

Answer: The intensity of the transmitted light is 75 units.

Why It Matters

Malus's Law is crucial in fields like optics and display technology. Engineers use it to design LCD screens for your mobile phones and TVs, ensuring clear images. It's also vital in medicine for understanding how light interacts with tissues in diagnostic tools, and for photographers using polarising filters to reduce glare.

Common Mistakes

MISTAKE: Using the angle between the *electric field vector* and the analyser axis. | CORRECTION: Malus's Law uses the angle between the *transmission axis of the incident polarised light* and the *transmission axis of the analyser*.

MISTAKE: Forgetting to square the cosine term (cos(theta) instead of cos^2(theta)). | CORRECTION: Always remember the 'square' part in 'cosine squared' (cos^2(theta)) as it's fundamental to the law.

MISTAKE: Applying Malus's Law to unpolarised light directly. | CORRECTION: Malus's Law applies ONLY to incident *polarised* light. If the incident light is unpolarised, its intensity becomes half after passing through the first polariser (I_0/2), and *then* Malus's Law applies for the second polariser.

Practice Questions

Try It Yourself

QUESTION: A beam of polarised light with an intensity of 80 W/m^2 passes through an analyser. If the angle between their transmission axes is 0 degrees, what is the transmitted intensity? | ANSWER: 80 W/m^2

QUESTION: Polarised light of intensity 120 units passes through an analyser. If the transmitted intensity is 30 units, what is the angle between the transmission axes of the light and the analyser? | ANSWER: 60 degrees

QUESTION: Unpolarised light of intensity 200 W/m^2 first passes through a polariser, and then through an analyser. If the angle between the polariser and analyser is 45 degrees, what is the final transmitted intensity? | ANSWER: 50 W/m^2

MCQ

Quick Quiz

According to Malus's Law, if the angle between the transmission axis of polarised light and the analyser is 90 degrees, what will be the transmitted intensity?

Maximum intensity

Half of the initial intensity

Zero intensity

Double the initial intensity

The Correct Answer Is:

When the angle is 90 degrees, cos(90) = 0. Therefore, cos^2(90) = 0, leading to zero transmitted intensity as per Malus's Law (I = I_0 * 0). This is called cross-polarisation.

Real World Connection

In the Real World

Next time you watch your favourite movie on an LED TV or use your smartphone, remember Malus's Law! The liquid crystal display (LCD) panels in these devices use polarisers to control the light passing through, creating the vibrant images you see. Without understanding this law, engineers couldn't design these everyday gadgets.

Key Vocabulary

Key Terms

POLARISED LIGHT: Light waves vibrating in a single plane. | UNPOLARISED LIGHT: Light waves vibrating in all possible planes. | POLARISER: A device that converts unpolarised light into polarised light. | ANALYSER: A second polariser used to determine the plane of polarisation or measure intensity changes. | INTENSITY: The power per unit area carried by the light wave.

What's Next

What to Learn Next

Now that you understand Malus's Law, you're ready to explore how polarisers are made and their practical applications, such as in 3D glasses or anti-glare filters. This will deepen your understanding of light and its amazing properties!