From e906a5149a0a9c116e1a3dbade6eb6ea659ac68a Mon Sep 17 00:00:00 2001 From: SparshRastogi <75373475+SparshRastogi@users.noreply.github.com> Date: Thu, 27 Oct 2022 16:52:10 +0530 Subject: [PATCH] Create malus_law.py (#7710) * Create malus_law.py Finding the intensity of light transmitted through a polariser using Malus Law and by taking initial intensity and angle between polariser and axis as input * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * Update physics/malus_law.py Co-authored-by: Caeden Perelli-Harris * Update physics/malus_law.py Co-authored-by: Caeden Perelli-Harris * Update physics/malus_law.py Co-authored-by: Caeden Perelli-Harris * Update physics/malus_law.py Co-authored-by: Caeden Perelli-Harris * Update malus_law.py Made some changes in the error messages and the docstring testcases * Update malus_law.py Made changes for the passing the precommit * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com> Co-authored-by: Caeden Perelli-Harris --- physics/malus_law.py | 80 ++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 80 insertions(+) create mode 100644 physics/malus_law.py diff --git a/physics/malus_law.py b/physics/malus_law.py new file mode 100644 index 000000000..ae77d45cf --- /dev/null +++ b/physics/malus_law.py @@ -0,0 +1,80 @@ +import math + +""" +Finding the intensity of light transmitted through a polariser using Malus Law +and by taking initial intensity and angle between polariser and axis as input + +Description : Malus's law, which is named after Étienne-Louis Malus, +says that when a perfect polarizer is placed in a polarized +beam of light, the irradiance, I, of the light that passes +through is given by + I=I'cos²θ +where I' is the initial intensity and θ is the angle between the light's +initial polarization direction and the axis of the polarizer. +A beam of unpolarized light can be thought of as containing a +uniform mixture of linear polarizations at all possible angles. +Since the average value of cos²θ is 1/2, the transmission coefficient becomes +I/I' = 1/2 +In practice, some light is lost in the polarizer and the actual transmission +will be somewhat lower than this, around 38% for Polaroid-type polarizers but +considerably higher (>49.9%) for some birefringent prism types. +If two polarizers are placed one after another (the second polarizer is +generally called an analyzer), the mutual angle between their polarizing axes +gives the value of θ in Malus's law. If the two axes are orthogonal, the +polarizers are crossed and in theory no light is transmitted, though again +practically speaking no polarizer is perfect and the transmission is not exactly +zero (for example, crossed Polaroid sheets appear slightly blue in colour because +their extinction ratio is better in the red). If a transparent object is placed +between the crossed polarizers, any polarization effects present in the sample +(such as birefringence) will be shown as an increase in transmission. +This effect is used in polarimetry to measure the optical activity of a sample. +Real polarizers are also not perfect blockers of the polarization orthogonal to +their polarization axis; the ratio of the transmission of the unwanted component +to the wanted component is called the extinction ratio, and varies from around +1:500 for Polaroid to about 1:106 for Glan–Taylor prism polarizers. + +Reference : "https://en.wikipedia.org/wiki/Polarizer#Malus's_law_and_other_properties" +""" + + +def malus_law(initial_intensity: float, angle: float) -> float: + """ + >>> round(malus_law(10,45),2) + 5.0 + >>> round(malus_law(100,60),2) + 25.0 + >>> round(malus_law(50,150),2) + 37.5 + >>> round(malus_law(75,270),2) + 0.0 + >>> round(malus_law(10,-900),2) + Traceback (most recent call last): + ... + ValueError: In Malus Law, the angle is in the range 0-360 degrees + >>> round(malus_law(10,900),2) + Traceback (most recent call last): + ... + ValueError: In Malus Law, the angle is in the range 0-360 degrees + >>> round(malus_law(-100,900),2) + Traceback (most recent call last): + ... + ValueError: The value of intensity cannot be negative + >>> round(malus_law(100,180),2) + 100.0 + >>> round(malus_law(100,360),2) + 100.0 + """ + + if initial_intensity < 0: + raise ValueError("The value of intensity cannot be negative") + # handling of negative values of initial intensity + if angle < 0 or angle > 360: + raise ValueError("In Malus Law, the angle is in the range 0-360 degrees") + # handling of values out of allowed range + return initial_intensity * (math.cos(math.radians(angle)) ** 2) + + +if __name__ == "__main__": + import doctest + + doctest.testmod(name="malus_law")