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81 lines
3.3 KiB
Python
81 lines
3.3 KiB
Python
import math
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"""
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Finding the intensity of light transmitted through a polariser using Malus Law
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and by taking initial intensity and angle between polariser and axis as input
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Description : Malus's law, which is named after Étienne-Louis Malus,
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says that when a perfect polarizer is placed in a polarized
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beam of light, the irradiance, I, of the light that passes
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through is given by
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I=I'cos²θ
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where I' is the initial intensity and θ is the angle between the light's
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initial polarization direction and the axis of the polarizer.
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A beam of unpolarized light can be thought of as containing a
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uniform mixture of linear polarizations at all possible angles.
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Since the average value of cos²θ is 1/2, the transmission coefficient becomes
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I/I' = 1/2
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In practice, some light is lost in the polarizer and the actual transmission
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will be somewhat lower than this, around 38% for Polaroid-type polarizers but
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considerably higher (>49.9%) for some birefringent prism types.
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If two polarizers are placed one after another (the second polarizer is
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generally called an analyzer), the mutual angle between their polarizing axes
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gives the value of θ in Malus's law. If the two axes are orthogonal, the
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polarizers are crossed and in theory no light is transmitted, though again
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practically speaking no polarizer is perfect and the transmission is not exactly
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zero (for example, crossed Polaroid sheets appear slightly blue in colour because
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their extinction ratio is better in the red). If a transparent object is placed
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between the crossed polarizers, any polarization effects present in the sample
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(such as birefringence) will be shown as an increase in transmission.
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This effect is used in polarimetry to measure the optical activity of a sample.
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Real polarizers are also not perfect blockers of the polarization orthogonal to
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their polarization axis; the ratio of the transmission of the unwanted component
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to the wanted component is called the extinction ratio, and varies from around
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1:500 for Polaroid to about 1:106 for Glan-Taylor prism polarizers.
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Reference : "https://en.wikipedia.org/wiki/Polarizer#Malus's_law_and_other_properties"
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"""
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def malus_law(initial_intensity: float, angle: float) -> float:
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"""
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>>> round(malus_law(10,45),2)
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5.0
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>>> round(malus_law(100,60),2)
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25.0
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>>> round(malus_law(50,150),2)
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37.5
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>>> round(malus_law(75,270),2)
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0.0
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>>> round(malus_law(10,-900),2)
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Traceback (most recent call last):
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...
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ValueError: In Malus Law, the angle is in the range 0-360 degrees
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>>> round(malus_law(10,900),2)
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Traceback (most recent call last):
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...
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ValueError: In Malus Law, the angle is in the range 0-360 degrees
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>>> round(malus_law(-100,900),2)
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Traceback (most recent call last):
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...
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ValueError: The value of intensity cannot be negative
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>>> round(malus_law(100,180),2)
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100.0
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>>> round(malus_law(100,360),2)
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100.0
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"""
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if initial_intensity < 0:
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raise ValueError("The value of intensity cannot be negative")
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# handling of negative values of initial intensity
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if angle < 0 or angle > 360:
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raise ValueError("In Malus Law, the angle is in the range 0-360 degrees")
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# handling of values out of allowed range
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return initial_intensity * (math.cos(math.radians(angle)) ** 2)
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if __name__ == "__main__":
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import doctest
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doctest.testmod(name="malus_law")
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