diff --git a/physics/diffraction.py b/physics/diffraction.py new file mode 100644 index 000000000000..dc5ba9577321 --- /dev/null +++ b/physics/diffraction.py @@ -0,0 +1,106 @@ +import math + + +def check_min_intensity( + slit_width: float = 1.0, diff_angle: float = 0.0, wavelength: float = 100.0 +) -> bool: + """ + Checks for the condition of minimum intensity in a diffraction pattern. + + Args: + slit_width (float): The width of the slit in millimeters. + diff_angle (float): The diffraction angle in radians. + wavelength (float): The wavelength of light in nanometers. + + Returns: + bool: True if minimum intensity is met, otherwise False. + + >>> check_min_intensity(4, 0.25, 300) + False + >>> check_min_intensity(1, 0.0001, 100) + True + """ + wavelength *= 10**-6 + n_val = round(slit_width * (diff_angle) / wavelength, 5) + r_val = n_val - math.floor(n_val) == 0 + return r_val + + +def check_max_intensity( + slit_width: float = 1.0, diff_angle: float = 0.0, wavelength: float = 100.0 +) -> bool: + """ + Checks for the condition of maximum intensity in a diffraction pattern. + + Args: + slit_width (float): The width of the slit in millimeters. + diff_angle (float): The diffraction angle in radians. + wavelength (float): The wavelength of light in nanometers. + + Returns: + bool: True if maximum intensity is met, otherwise False. + + >>> check_max_intensity(1, 0.001, 100) + False + >>> check_max_intensity(1, 0.00005, 100) + True + """ + wavelength *= 10**-6 + n_val = round(((2 * slit_width * diff_angle) - wavelength) / (2 * wavelength), 4) + r_val = n_val - math.floor(n_val) == 0 + return r_val + + +def intensity_single_slit( + slit_width: float = 1.0, diff_angle: float = 0.0, wavelength: float = 100.0 +) -> str: + """ + Computes the intensity for a single slit diffraction pattern. + + Args: + slit_width (float): The width of the slit in millimeters. + diff_angle (float): The diffraction angle in radians. + wavelength (float): The wavelength of light in nanometers. + + Returns: + str: The intensity of the diffraction pattern. + + >>> intensity_single_slit(1, 0.0005, 100) + '0.9999999999177533 I0' + """ + beta = math.pi * slit_width * (math.sin(diff_angle) / wavelength) + i_coeff = (math.sin(beta) / beta) ** 2 + return f"{i_coeff} I0" + + +def intensity_double_slit(path_diff: int = 0, intensity_max: str | float = "I0") -> str: + """ + Computes the intensity for a double slit diffraction pattern. + + Args: + path_diff (float): The path difference in the two waves. + intensity_max (str or int): The maximum intensity. + + Returns: + str or float: The intensity of the diffraction pattern. + + >>> intensity_double_slit(0, 1) + '4.0' + >>> intensity_double_slit(0.001, 1) + '3.999999000000084' + >>> intensity_double_slit(0) + '4.0 I0' + """ + r_val = ( + str(4 * intensity_max * (math.cos(path_diff / 2)) ** 2) + if (type(intensity_max) is float or type(intensity_max) is int) + else f"{4*(math.cos(path_diff/2)**2)} I0" + ) + return r_val + + +if __name__ == "__main__": + import doctest + + doctest.testmod() + # pass