# Malus Law Formula, Calculator, Calculation of Output Intensity

### Malus Law Calculator:

A Malus law calculator is a useful tool for explaining the working principle of polarizers. Depending on the relative position between the light polarization direction and the polarizer axis, different amounts of light can be transmitted. By knowing the initial intensity and polarization orientation of the light, the output intensity from polarization can be easily determined based on Malus’ law.

Light can be described as mutually oscillating electric and magnetic fields creating an electromagnetic wave. These oscillations are perpendicular to each other and simultaneously perpendicular to the direction of wave propagation.

Light is said to be linearly polarized if the orientation of the oscillations is constant over time. It is common to say that the direction of light polarization is the same as the direction of electric field oscillations.

Polarized light can be obtained if the angle of incidence is equal to Brewster’s angle or by passing the light through some dichroic crystal due to reflection at the boundary of two media having different refractive indices.

### Malus  Law Formula:

Malus law formula is used to calculate the output irradiance Intensity(w/m2) in watts per meter2 is equal to the  irradiance of incident light initial – intensity(w/m2)  in watts per meter2 and multiply  square of the angle between the light polarization and the axis of the polarizer cos2 θ(d).Hence the malus Law formula can be written as

Intensity(w/m2) =initial – intensity(w/m2)  * cos2 θ(d)

Where,

Initial –intensity is the irradiance of incident light

Θ= is the angle between the light polarization and the axis of the polarizer

### Example:1

Two polaroids A and B kept with their transmission axes at an angle of 40 degrees with respect to other.If the intensity of the light incident on the system is 4w/m2,find the  transmitted intensity of light?

Given that

Initial intensity=4w/m2

Θ=40 degrees

Malus Law formula is intensity =initial – intensity * cos²θ

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Intensity =4* cos2 (40)

=4* cos2 (40)

=2.3489 w/m2

### Example:2

Two polaroids A and B kept with their transmission axes at an angle of 60 degrees with respect to other.If the intensity of the light incident on the system is 8w/m2,find the  transmitted intensity of light?

Given that

Initial intensity=8w/m2

Θ=60 degrees

Malus Law formula is intensity =initial – intensity * cos²θ

Intensity =8* cos2 (60)

=8* cos2 (60)

=2.0036 w/m2