Create bragg_angle.py (#11744)

* Create bragg_angle.py

* [pre-commit.ci] auto fixes from pre-commit.com hooks

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* updating DIRECTORY.md

---------

Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Co-authored-by: Christian Clauss <cclauss@me.com>
Co-authored-by: cclauss <cclauss@users.noreply.github.com>

DIRECTORY.md

@@ -1008,6 +1008,7 @@
   * [Altitude Pressure](physics/altitude_pressure.py)
   * [Archimedes Principle Of Buoyant Force](physics/archimedes_principle_of_buoyant_force.py)
   * [Basic Orbital Capture](physics/basic_orbital_capture.py)
+  * [Bragg Angle](physics/bragg_angle.py)
   * [Casimir Effect](physics/casimir_effect.py)
   * [Center Of Mass](physics/center_of_mass.py)
   * [Centripetal Force](physics/centripetal_force.py)

physics/bragg_angle.py

@@ -0,0 +1,41 @@
+import math
+
+
+def bragg_angle(distance: float, order: int, wavelength: float) -> float:
+    """
+    Calculate the Bragg diffraction angle using the formula:
+    sin(θ) = (n * λ) / (2 * d)
+
+    Parameters:
+    distance d (float): Distance between crystal planes (in meters).
+    order n (int): Order of reflection.
+    wavelength λ (float): Wavelength of the radiation (in meters).
+
+    Examples:
+    >>> bragg_angle(2.2e-10, 1, 2.2e-10)
+    30.0
+
+    >>> bragg_angle(5e-10, 2, 1e-10)
+    11.5
+
+    >>> bragg_angle(4e-10, 1, 4e-10)
+    30.0
+
+    # Test case for an invalid sine value (out of range)
+    >>> bragg_angle(1e-10, 2, 3e-10)
+    Traceback (most recent call last):
+        ...
+    ValueError: The calculated sine value is out of the valid range.
+    """
+    sine_theta = (order * wavelength) / (2 * distance)
+    if sine_theta > 1 or sine_theta < -1:
+        raise ValueError("The calculated sine value is out of the valid range.")
+    theta_radians = math.asin(sine_theta)
+    theta_degrees = math.degrees(theta_radians)
+    return round(theta_degrees, 1)
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod(verbose=True)