Create malus_law.py

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")