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
Full video and playlists:
- Full video:
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