Added optika.materials.snells_law_scalar function.

optika/materials/__init__.py

@@ -3,7 +3,10 @@
 or reflective materials.
 """
 
-from ._snells_law import snells_law
+from ._snells_law import (
+ snells_law_scalar,
+ snells_law,
+)
 from . import profiles
 from . import matrices
 from ._layers import (
@@ -36,6 +39,7 @@
 )
 
 __all__ = [
+ "snells_law_scalar",
  "snells_law",
  "profiles",
  "matrices",

optika/materials/_snells_law.py

@@ -4,10 +4,37 @@
 import named_arrays as na
 
 __all__ = [
+ "snells_law_scalar",
  "snells_law",
 ]
 
 
+def snells_law_scalar(
+ cos_incidence: float | na.AbstractScalar,
+ index_refraction: float | na.AbstractScalar,
+ index_refraction_new: float | na.AbstractScalar,
+) -> na.AbstractScalar:
+ """
+ A simple form of Snell's law which computes the cosine of the angle
+ between the propagation direction inside the new medium and the interface
+ normal.
+
+ Parameters
+ ----------
+ cos_incidence
+ The cosine of the incidence angle (the angle between the propagation
+ direction and the interface normal.)
+ index_refraction
+ The index of refraction in the current medium.
+ index_refraction_new
+ The index of refraction in the new medium.
+ """
+ sin_incidence = np.sqrt(1 - np.square(cos_incidence))
+ sin_transmitted = index_refraction * sin_incidence / index_refraction_new
+ cos_transmitted = np.sqrt(1 - np.square(sin_transmitted))
+ return cos_transmitted
+
+
 def snells_law(
  wavelength: u.Quantity | na.AbstractScalar,
  direction: na.AbstractCartesian3dVectorArray,

optika/materials/_tests/test_snells_law.py

@@ -5,6 +5,44 @@
 import optika
 
 
+@pytest.mark.parametrize(
+ argnames="cos_incidence",
+ argvalues=[
+ 1,
+ na.linspace(-1, 1, axis="angle", num=7),
+ ],
+)
+@pytest.mark.parametrize(
+ argnames="index_refraction",
+ argvalues=[
+ 1,
+ ],
+)
+@pytest.mark.parametrize(
+ argnames="index_refraction_new",
+ argvalues=[
+ 1.5,
+ na.linspace(1, 2, axis="index_refraction_new", num=4),
+ ],
+)
+def test_snells_law_scalar(
+ cos_incidence: float | na.AbstractScalar,
+ index_refraction: float | na.AbstractScalar,
+ index_refraction_new: float | na.AbstractScalar,
+):
+ result = optika.materials.snells_law_scalar(
+ cos_incidence=cos_incidence,
+ index_refraction=index_refraction,
+ index_refraction_new=index_refraction_new,
+ )
+
+ n1 = index_refraction
+ n2 = index_refraction_new
+ result_expected = np.cos(np.arcsin(n1 * np.sin(np.arccos(cos_incidence)) / n2))
+
+ assert np.allclose(result, result_expected)
+
+
 @pytest.mark.parametrize(
  argnames="wavelength",
  argvalues=[