# Wien's Displacement and Rayleigh-Jeans Law from Planck's Law

I've derived Planck's Law for frequency from his law for wavelength, and I got this: $$u(f)=\frac {8\pi f^2} {c^3} \frac {hf} {e^{\frac {hf}{kT}}-1}$$

I just have a quick question about this. This problem says I need to find the low-frequency limit (which will lead to the Rayleigh-Jeans), and I need to take the high-frequency limit, which is supposed to lead to Wien's distribution.

The thing is I have no idea what the high, or low frequency limit even means, I've looked in my book, I've looked online, I'm not sure exactly what it means.

• For high frequency limit, $hf>>kT$ and for low frequency limits, $hf<<kT$. What effect these arguments produce on the exponential term? – UKH Sep 22 '16 at 5:14

If we take the low frequency limit, i.e. $hf\ll kT$, then we can expand the exponential $$e^x\ =\ 1\ +\ x\ +\ \frac{x^2}{2}\ +\ \ldots$$ and truncate the series at $x$ ignoring the higher order terms. This will gives us the Rayleigh-Jeans law.
Next, if we take the high frequency limit, where $hf\gg kT$, we can ignore the $1$ in the denominator. This leads to the Wien's law.