# Malus Law - Cosine squared term?

• Dart82
In summary, the conversation discusses Malus law in physics and the formula S = s*cos^2(theta). The question is asked about the meaning of the cosine squared term in the equation and whether it is the same as [cos(theta)]^2. The response clarifies that it is an unfortunate notation that can cause confusion and explains the different ways it can be written. The conversation concludes with the clarification being appreciated.

#### Dart82

this is just a general trig question:

We are going over Malus law in physics; the formula is this:
S = s*cos^2(theta)

My question is about the cosine squared term in the equation. does this simply mean take the cosine of a number and square it? in other words would this be the same thing as [cos(theta)]^2

Indeed!

It is an unfortunate notation that confuses a lot of students, but it won't ever go away. you have to live with it.

I simply tell my students that once upon a time, they wrote it as (sinx)^2, but lazy students kept leaving off the parenthesis and wrote sinx^2, sometimes meaning to take the sine of x, then square that answer; other times meaning to square the x first, then take the sine. To eliminate confusion, when they want the sin value to be squared, they put the squared symbol right next to sin
$$sin^{2}x$$

So, to shorten $$(sinx)^2$$ write $$sin^{2}x$$
and
to shorten $$sin(x^2)$$ write $$sinx^2$$ (although some people prefer those parenthesis are left in the latter case.)

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ahhh...thanks for the clarification guys. you've made my day a lot easier!

## 1. What is Malus Law?

Malus Law is a phenomenon in physics that describes the relationship between the intensity of polarized light and the angle at which it is transmitted or reflected through a polarizing filter.

## 2. What is the cosine squared term in Malus Law?

The cosine squared term in Malus Law refers to the mathematical formula used to calculate the intensity of polarized light after it passes through a polarizing filter at a certain angle. The formula is I = I0cos2θ, where I0 is the initial intensity and θ is the angle between the polarization direction of the filter and the direction of the incident light.

## 3. How is Malus Law related to the properties of light?

Malus Law is related to the properties of light because it explains how polarized light behaves when it passes through a polarizing filter. It takes into account the polarization direction of the filter and the angle at which the light is transmitted or reflected, which are both properties of light.

## 4. What is the significance of Malus Law?

Malus Law is significant because it helps scientists and engineers understand and predict the behavior of polarized light in various applications. It is also used in polarimetry, a technique for measuring the polarization state of light.

## 5. How is Malus Law used in everyday life?

Malus Law is used in everyday life in various applications, such as sunglasses, 3D glasses, and LCD screens. These technologies utilize polarizing filters to block or transmit certain polarized light, and Malus Law helps in understanding and optimizing their performance.