Malus Law Formula

Malus noticed that when the crystal spun, the intensity changed from highest to minimum. Consequently, he suggested that A = A cosθ must be the amplitude of the reflected beam. Malus calculated the intensity by square-rooting the amplitude relation i.e. I_o = A_o².

I(θ) = I_o cos² θ

Where

• I is the transmitted light intensity,
• I_o is the initial light intensity, and
• θ is the angle between the light’s initial polarization direction and the axis of the polarizer.

This equation is known as Malus’s Law.

Derivation of Malus Law Formula

Assume the light source emits unpolarized light, which means the electric field vector oscillates randomly in all directions perpendicular to the direction of propagation.

When this light encounters a polarizing filter, the filter only allows the component of the electric field parallel to its polarization axis to pass through.

The electric field vector of the incoming light can be represented as = E₀​cos(ωt−kx) , where:

• E₀​ is the amplitude of the electric field,
• ω is the angular frequency of the light,
• k is the wave number,
• x is the position,
• t is the time, and
• is a unit vector in the direction of the electric field.

When the light hits the polarizer, the electric field vector can be decomposed into two components: parallel (E_∥​) and perpendicular (E_⊥​) to the axis of the polarizer. Since the perpendicular component is blocked, only E_∥​ passes through.

If θ is the angle between the light’s initial polarization direction and the axis of the filter, the parallel component is given by E_∥​=E₀​cos(θ).

The intensity of light is proportional to the square of the amplitude of its electric field. If I₀​ is the intensity of the incident light, the intensity I of the transmitted light is proportional to E_∥²​.

Therefore, the intensity of the light after passing through the polarizer is I = I_o cos² θ.

Malus Law, also known as Malus Law of Polarization, is a fundamental principle in optics that describes how the intensity of polarized light changes as it passes through a polarizer. It is named after Étienne-Louis Malus, a French physicist who formulated the law in 1808.

In this article, we will discuss the concept of Malus Law which describes the intensity of change in the intensity of polarized light.