Short Answer
Malus’ law is a principle in optics that describes how the intensity of plane-polarized light changes when it passes through a polarizing filter (analyzer) at an angle. According to the law, the transmitted intensity depends on the square of the cosine of the angle between the light’s vibration plane and the axis of the polarizer.
Mathematically, I = I₀ cos²θ, where I₀ is the initial intensity and θ is the angle. Malus’ law is essential in understanding polarization, designing optical instruments, and controlling light intensity.
Detailed Explanation :
Malus’ Law
Malus’ law, named after the French physicist Étienne-Louis Malus, is a fundamental law of polarization of light. It provides a quantitative relationship between the intensity of polarized light and the angle between the light’s vibration plane and the transmission axis of a polarizing filter.
The law is applicable only to plane-polarized light, where the electric field vectors vibrate in a single plane. Unpolarized light must first be converted to plane-polarized light using a polarizer before Malus’ law can be applied.
Statement of Malus’ Law
When plane-polarized light of intensity I₀ passes through a polarizer (analyzer) at an angle θ to the light’s plane of vibration:
Where:
- I = transmitted intensity
- I₀ = initial intensity of plane-polarized light
- θ = angle between the plane of polarization and the axis of the analyzer
Key points:
- Maximum intensity occurs when θ = 0° (planes aligned).
- No light is transmitted when θ = 90° (planes perpendicular).
- The transmitted intensity varies continuously with the cosine squared of the angle.
Explanation of the Law
- Plane-Polarized Light:
Light has electric field vectors vibrating in a single plane. - Analyzer:
A polarizing filter allows only the component of the electric field along its axis to pass. - Component of Electric Field:
If E₀ is the amplitude of the incident electric field, the component along the analyzer axis is:
E = E₀ cos θ - Intensity Relation:
Since intensity is proportional to the square of the electric field, I ∝ E², we get:
I = I₀ cos² θ
This is Malus’ law in mathematical form.
Experimental Verification
- A polarized light source (like a Polaroid sheet) is used.
- The light passes through an analyzer (second polarizer).
- The analyzer is rotated through different angles.
- The transmitted light intensity is measured.
- The intensity is found to follow I = I₀ cos² θ, confirming Malus’ law.
Applications of Malus’ Law
- Controlling Light Intensity:
- Used in polarizing filters in photography and LCD screens.
- Rotating the analyzer adjusts brightness according to cos² θ.
- Optical Instruments:
- In polarimeters, Malus’ law helps measure optical rotation of substances.
- Scientific Research:
- Used to study polarization properties of light in experiments.
- Reducing Glare:
- Polarized sunglasses work on the principle of controlling light intensity.
- Holography and Lasers:
- Helps in controlling intensity of coherent, plane-polarized light for precise interference patterns.
Graphical Representation
- A plot of transmitted intensity I vs. angle θ shows a cos² θ curve.
- Maximum intensity at 0° and 180°; minimum intensity at 90° and 270°.
- This pattern is used to determine polarization angles and measure light intensity.
Conclusion
Malus’ law is a key principle describing how the intensity of plane-polarized light varies with the angle of a polarizing filter. It states that the transmitted intensity is proportional to the cosine squared of the angle between the light’s vibration plane and the polarizer axis. Malus’ law is widely used in optics, photography, polarimetry, and laser applications to control light intensity and study polarization. It also provides experimental proof of the transverse nature of light waves and the behavior of polarized light.