Rayleigh-Jeans law VS Planck's law
通过将指数函数展开成数列形式,用极限证明波长$\lambda$是很长的,并且普朗克定律(Planck's law)收敛于瑞利—琼斯定律(Rayleigh-Jeans law).
The series expansion for $e^x$ is:
$$e^x=\sum_{j=0}^{\infty}\frac{x^j}{j!}$$
Rayleigh-Jeans law is:
$$I(\lambda,T)=\dfrac{2\pi ckT}{\lambda^4}$$
Planck's law is:
$$I(\lambda,T)=\dfrac{2\pi hc^2}{\lambda^5(e^\frac{hc}{\lambda kT}-1)}$$
|