Blackbody Radiation Question 2: Planck's Law Approximates Rayleigh-Jeans Law at Large Wavelengths

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2024-05-29 15:39

In this video I show that using just the first term for the Taylor series expansion of the exponential function in Planck's Law, it becomes Rayleigh-Jeans Law. This results in a good approximation for Rayleigh-Jeans Law at large wavelengths since the extra terms of the Taylor series become very small.

Timestamps:

Question 2: Using Taylor polynomials, Planck's Law approximates Rayleigh-Jeans Law at large wavelengths: 0:00
Solution: Approximating exponential function using Taylor series: 0:28
Recap on Taylor series: 0:56
Exponential function as a Taylor series: 2:40
Approximating Planck's Law using Taylor series for Exponential function: 4:03
Approximating Taylor series for large wavelengths: 5:58
Large wavelength approximation for Planck's Law: 6:40
Canceling out terms of Planck's Law to get Rayleigh-Jeans Law: 8:36
Summary: Using the first non-zero term of Taylor series only approximates Rayleigh-Jeans Law: 9:44

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