How to Derive Malus' Law for Two Polarizers Using Integrals?

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In summary, Malus' Law is a scientific law that explains the relationship between the intensity of polarized light and the angle at which it passes through a polarizer. It was discovered by French physicist Etienne-Louis Malus in 1808. The law is derived using the principles of wave optics and the properties of polarized light, and assumes that the incident light is polarized, the polarizer is ideal and has a perfect transmission axis, and the polarizer and analyzer are orthogonal. Malus' Law has various applications in optics, astronomy, and telecommunications, and can also be used to calculate the degree of polarization.
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Arman777
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Is there any source that how can I derive the Malus of ?
Where there's two polarizer

This is the equation
$$I_{out}=I_{in}[H_{90}+(H_0-H_{90})]cos^2(θ)$$

##H_0=1/2(k_1^2+k_2^2)## and ##H_{90} = k_1k_2##

Also I need to derive the $$I_{out}=1/2I_{in}cos^2θ$$ using integrals

Please help
 
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Renu5678 said:
Are there any additional conditions?
I don't think so no. We made an experiment and in the theory part I need to write the derivation but I couldn't find any source of it. This is the general condiiton I guess ?
 

1. What is Malus' Law?

Malus' Law is a scientific law that describes the relationship between the intensity of polarized light and the angle at which it passes through a polarizer. It was discovered by French physicist Etienne-Louis Malus in 1808.

2. How is Malus' Law derived?

To derive Malus' Law, we use the principles of wave optics and the properties of polarized light. This involves using the equation for the intensity of light to determine how much light is transmitted through a polarizer at different angles.

3. What are the assumptions made in the derivation of Malus' Law?

The derivation of Malus' Law assumes that the incident light is polarized, the polarizer is ideal and has a perfect transmission axis, and the polarizer and analyzer are orthogonal.

4. What are the applications of Malus' Law?

Malus' Law has several applications in various fields, including optics, astronomy, and telecommunications. It is used to analyze polarized light in experiments and to design and calibrate optical instruments.

5. Can Malus' Law be used to calculate the degree of polarization?

Yes, Malus' Law can be used to calculate the degree of polarization by measuring the intensity of polarized light at different angles and using the equation for Malus' Law to determine the degree of polarization. It is a valuable tool in studying and analyzing polarized light.

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