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The Rayleigh-Jeans Law is a fundamental concept in classical physics, relating to the spectral radiance of black body radiation. It connects energy density with frequency and temperature, and while it succeeds at low frequencies, it fails at high frequencies, leading to the ultraviolet catastrophe. This law's limitations were instrumental in the development of quantum mechanics and continue to influence scientific and technological applications.

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## Formulation and Significance of the Rayleigh-Jeans Law

### Definition and Equation

The Rayleigh-Jeans Law is an equation that relates the energy density of electromagnetic radiation from a black body to its frequency and temperature

### Failure at High Frequencies and the Ultraviolet Catastrophe

Role in the Development of Quantum Mechanics

The Rayleigh-Jeans Law's inability to accurately predict radiation intensity at high frequencies led to the development of quantum mechanics

### Derivation and Assumptions

The Rayleigh-Jeans Law is derived from classical statistical mechanics and wave theory, assuming that energy is equally distributed among all degrees of freedom in a system at thermal equilibrium

## Comparison with Wien's Displacement Law and Unification under Planck's Law

### Wien's Displacement Law

Wien's Law accurately describes radiation at higher frequencies, while the Rayleigh-Jeans Law is applicable at lower frequencies

### Planck's Law of Black-Body Radiation

Simplification to the Rayleigh-Jeans Law

Planck's Law simplifies to the Rayleigh-Jeans Law at long wavelengths or low frequencies, leading to the unification of these laws

### Importance in Modern Physics

The unification of the Rayleigh-Jeans Law and Wien's Displacement Law under Planck's quantum theory marked a significant advancement in modern physics

## Practical Applications of the Rayleigh-Jeans Law

### Astrophysics and Environmental Science

The Rayleigh-Jeans Law is used to model the emission spectra of stars and galaxies, aiding in the study of the universe and contributing to our understanding of the Earth's radiation balance

### Technological Applications

The Rayleigh-Jeans Law informs the design of devices such as thermal cameras and radiation sensors

### Limitations and Continued Relevance

Despite its theoretical limitations, the Rayleigh-Jeans Law remains a valuable tool in both scientific inquiry and technological innovation

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