Malus Law Calculator

Malus's Law states that when completely plane-polarized light is incident on an analyzer, the resultant intensity ($I$) of transmitted light varies directly as the square of the cosine of the angle ($\theta$) between the transmission axis of the analyzer and the polarizer. The fundamental formula governing this relationship is expressed as $I = I_0 \cdot \cos^2(\theta)$, where $I_0$ represents the initial peak intensity of the incident polarized beam, and $\theta$ is the angle of rotation.

Imagine you are working in an optical laboratory with an initial polarized light beam having an intensity ($I_0$) of 150 watts per square meter ($W/m^2$). You rotate your analyzer filter to an angle ($\theta$) of 30 degrees relative to the polarization axis. To find the transmitted intensity, first convert the angle to radians or evaluate the cosine directly. The cosine of 30 degrees is approximately 0.866. Squaring this value yields $(0.866)^2 = 0.75$. Multiplying this result by the initial intensity gives $I = 150 \cdot 0.75 = 112.5 \text{ W/m}^2$. Thus, the transmitted light intensity is 112.5 watts per square meter.

Always verify whether your input angle is in degrees or radians before computing the cosine function to avoid severe calculation errors. Ensure that your initial intensity ($I_0$) uses consistent units, such as candelas, lumens, or watts per square meter, to keep your resulting output physically meaningful. When setting up multi-stage polarization systems, remember to apply Malus's law sequentially at each successive polarizing filter.