Wien's Law

I am unable to understand the physical meaning of the two different forms of Wiens law even though I understand the mathematical derivations.

This predates quantum mechanics. It was known before Planck used quantum mechanics (actually, he helped invent it!) that the spectrum of a blackbody source of radiation (really, any source of a continuum spectrum) peaked at a specific wavelength. Wien quantified that and produced the equation: constant wavelength = -------- temp. where the constant is equal to 0.2898 centimeters-degree. Wien calculated this number simply by measuring the peak wavelengths of blackbodies of varying temperature in the laboratory.

Max Planck came along and, with the use of the idea that light is composed of photons and waves, showed why the so-called blackbody curve is shaped the way it is. Explaining that is way beyond the scope of this forum; I recommend you find a book about the discovery of quantum mechanics. Several such books can be found in bookstores or libraries. I would even go as far as to recommend a book written for the educated layman, as that is most likely to give a clear, concise explanation of how these discoveries came about. From there you can get as complicated as you'd like!

Probably the most common use for Wien's law today is in astronomy. Stars themselves produce a blackbody-like spectrum, and the surface temperature of a star is closely related to the color. Absorption of specific wavelengths in the star's atmosphere will make the spectrum deviate from a blackbody somewhat, but this is a relatively small effect compared to the overall spectrum.

If you have any other questions, or if this did not answer the question you had in mind, feel free to email me personally, or rephrase your question (perhaps giving the forms of Wien's law you mention) and resubmit it!