light-speed 0.1.2

A comprehensive physics package for light speed and real-world calculations

Light Speed Physics

light_speed is a comprehensive Python package for calculations and simulations related to the speed of light, relativistic physics, and real-world optical phenomena. It is designed for scientists, researchers, and physics enthusiasts who want to explore the fascinating world of light and its interactions.

---

Features

• Relativity Calculations:
  • Lorentz factor, time dilation, length contraction, relativistic mass, and momentum.
• Optics:
  • Snell's law, critical angle, and chromatic dispersion in fiber optics.
• Photon Energy:
  • Energy-wavelength conversions.
• Waveguides:
  • Supported modes in planar waveguides.
• Medium Properties:
  • Speed of light in various mediums, refractive index calculators, and Fresnel reflection coefficients.

---

Installation

Install the package using pip:

pip install light_speed

---

Usage

Import the Package

from light_speed import LightSpeedPhysics

Examples

1. Speed of Light in a Medium

Calculate the speed of light in a specific medium using its refractive index:

from light_speed import LightSpeedPhysics

physics = LightSpeedPhysics()
n_water = physics.refractive_index_calculator('water')
speed_water = physics.speed_in_medium(n_water)
print(f"Speed of light in water: {speed_water:.2f} m/s")

---

2. Relativistic Time Dilation

Compute the time dilation for an object moving at a significant fraction of the speed of light:

from light_speed import LightSpeedPhysics

physics = LightSpeedPhysics()
proper_time = 1.0  # seconds
velocity = 1e7  # m/s
dilated_time = physics.time_dilation(proper_time, velocity)
print(f"Dilated Time: {dilated_time:.2f} seconds")

---

3. Lorentz Factor

Calculate the Lorentz factor for a given velocity:

from light_speed import LightSpeedPhysics

physics = LightSpeedPhysics()
velocity = 1e7  # m/s
lorentz_factor = physics.lorentz_factor(velocity)
print(f"Lorentz Factor: {lorentz_factor:.2f}")

---

4. Length Contraction

Find the contracted length of a moving object:

from light_speed import LightSpeedPhysics

physics = LightSpeedPhysics()
proper_length = 10.0  # meters
velocity = 2e8  # m/s
contracted_length = physics.length_contraction(proper_length, velocity)
print(f"Contracted Length: {contracted_length:.2f} meters")

---

5. Relativistic Mass

Calculate the relativistic mass of an object:

from light_speed import LightSpeedPhysics

physics = LightSpeedPhysics()
rest_mass = 70.0  # kg
velocity = 2.5e8  # m/s
rel_mass = physics.relativistic_mass(rest_mass, velocity)
print(f"Relativistic Mass: {rel_mass:.2f} kg")

---

6. Relativistic Momentum

Determine the relativistic momentum of a moving object:

from light_speed import LightSpeedPhysics

physics = LightSpeedPhysics()
mass = 70.0  # kg
velocity = 2.5e8  # m/s
momentum = physics.relativistic_momentum(mass, velocity)
print(f"Relativistic Momentum: {momentum:.2e} kg⋅m/s")

---

7. Relativistic Kinetic Energy

Calculate the kinetic energy of an object moving at relativistic speeds:

from light_speed import LightSpeedPhysics

physics = LightSpeedPhysics()
mass = 70.0  # kg
velocity = 2e8  # m/s
kinetic_energy = physics.relativistic_kinetic_energy(mass, velocity)
print(f"Relativistic Kinetic Energy: {kinetic_energy:.2e} Joules")

---

8. Energy to Wavelength Conversion

Convert photon energy (in electron volts) to wavelength:

from light_speed import LightSpeedPhysics

physics = LightSpeedPhysics()
energy_ev = 2.0  # eV
wavelength = physics.energy_wavelength_conversion(energy_ev)
print(f"Wavelength: {wavelength:.2e} meters")

---

9. Snell's Law

Calculate the angle of refraction when light moves between two mediums:

from light_speed import LightSpeedPhysics

physics = LightSpeedPhysics()
theta1 = 30  # degrees
n1 = physics.refractive_index_calculator('air')
n2 = physics.refractive_index_calculator('glass')
theta2 = physics.snells_law(n1, n2, theta1)
print(f"Refraction Angle: {theta2:.2f} degrees")

---

10. Critical Angle

Determine the critical angle for total internal reflection:

from light_speed import LightSpeedPhysics

physics = LightSpeedPhysics()
critical_angle = physics.critical_angle(1.52, 1.000293)
print(f"Critical Angle: {critical_angle:.2f} degrees")

---

11. Fiber Optic Travel Time

Calculate the travel time of light through a fiber optic cable:

from light_speed import LightSpeedPhysics

physics = LightSpeedPhysics()
distance = 100000  # meters
core_index = 1.462
travel_time = physics.fiber_optic_travel_time(distance, core_index)
print(f"Travel Time: {travel_time * 1000:.2f} milliseconds")

---

12. Chromatic Dispersion

Calculate the time delay caused by chromatic dispersion in optical fibers:

from light_speed import LightSpeedPhysics

physics = LightSpeedPhysics()
wavelength1 = 1.55e-6  # meters
wavelength2 = 1.50e-6  # meters
fiber_length = 50000  # meters
time_delay = physics.chromatic_dispersion(wavelength1, wavelength2, fiber_length)
print(f"Chromatic Dispersion Time Delay: {time_delay:.2e} seconds")

---

13. Group Velocity

Compute the group velocity of a light pulse in a medium:

from light_speed import LightSpeedPhysics

physics = LightSpeedPhysics()
wavelength = 1.55e-6  # meters
dn_dlambda = -0.02  # change in refractive index per wavelength
group_velocity = physics.group_velocity(wavelength, dn_dlambda)
print(f"Group Velocity: {group_velocity:.2f} m/s")

---

14. Fresnel Reflection Coefficient

Calculate the Fresnel reflection coefficients:

from light_speed import LightSpeedPhysics

physics = LightSpeedPhysics()
n1 = 1.000293  # air
n2 = 1.52  # glass
theta_i = 45  # degrees
r_parallel, r_perpendicular = physics.reflection_coefficient(n1, n2, theta_i)
print(f"Reflection Coefficient (Parallel): {r_parallel:.2f}")
print(f"Reflection Coefficient (Perpendicular): {r_perpendicular:.2f}")

---

15. Waveguide Modes

Calculate the number of modes supported by a planar waveguide:

from light_speed import LightSpeedPhysics

physics = LightSpeedPhysics()
width = 5e-6  # meters
wavelength = 1.55e-6  # meters
n_core = 1.5
n_cladding = 1.4
modes = physics.waveguide_modes(width, wavelength, n_core, n_cladding)
print(f"Number of Modes: {modes}")

---

16. Doppler Shift

Calculate the relativistic Doppler shift for an approaching or receding source:

from light_speed import LightSpeedPhysics

physics = LightSpeedPhysics()
frequency = 500e12  # Hz
velocity = 2e7  # m/s
approaching = True  # True if approaching, False if receding
shifted_frequency = physics.doppler_shift(frequency, velocity, approaching)
print(f"Shifted Frequency: {shifted_frequency:.2f} Hz")

---

Requirements

• Python
• NumPy (automatically installed)

---

Contributing

Contributions are welcome! Follow these steps to contribute:

1. Fork the repository.
2. Create a feature branch (git checkout -b feature-name).
3. Commit your changes (git commit -m 'Add some feature').
4. Push to the branch (git push origin feature-name).
5. Open a pull request.

---

License

This project is licensed under the MIT License. See the LICENSE file for details.