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- Homework Statement
- Please see below

- Relevant Equations
- ##I= I_{max}\cos^2\theta## Where ##\theta## is the angle between the direction of propagation and axis of polarizer

I am trying to Derive Malus's Law. My textbook says that an electric field as an amplitude ##E## before passing thought the polarizer and reduce to ##E_{trans} = E\cos\theta##.

I am trying to understand why this occurs my considering a vertically polarized light passing though a polarizer that is at angle ##\phi## to the horizontal. The red line in the diagram below is the polarizer axis.

However, from the diagram, ##\cos\theta = \frac{E}{E_{trans}}## which rearranges to ##E_{trans} = \frac{E}{\cos\theta}## however, the component of the light transmitted should be ##E_{trans} = E\cos\theta##. Could some please give me some guidance on what I have done wrong?

NOTE: ##\theta## could also be ##\theta_2## since ##(\cos\theta_1)^2 = (\cos\theta_2)^2##

Many thanks!

I am trying to understand why this occurs my considering a vertically polarized light passing though a polarizer that is at angle ##\phi## to the horizontal. The red line in the diagram below is the polarizer axis.

However, from the diagram, ##\cos\theta = \frac{E}{E_{trans}}## which rearranges to ##E_{trans} = \frac{E}{\cos\theta}## however, the component of the light transmitted should be ##E_{trans} = E\cos\theta##. Could some please give me some guidance on what I have done wrong?

NOTE: ##\theta## could also be ##\theta_2## since ##(\cos\theta_1)^2 = (\cos\theta_2)^2##

Many thanks!

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