Uploaded March 2025 | Updated September 2026, 2 weeks ago

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Here is a part of the 2024 IPho International Physics Olympiad covering a question on the Greenhouse effect.
This olympiad question can be used for preparation for the IPhO and also for similar competitions as as the British Physics Olympiad, BPhO, American F=ma exam and Physics Olympiad. It is a great application of calculus based physics and it's also highly unusual in terms of the solutions.

The problem can be found here: ipho.olimpicos.net/pdf/IPhO_2024_Q1.pdf

Solution: ipho.olimpicos.net/pdf/IPhO_2024_S1.pdf

Please note this is not an official solution and I am not affiliated with the Ipho. Always be critical of solutions.

More on Feynman Differentiation: https://www.feynmanlectures.caltech.edu/TIPS_01.html#Ch1-S5 "Feynman's Tips on Physics, Chapter 1, Prerequisites - Review Lecture A"

Chapters:
00:00 Key Information
02:31 Finding the intensity near Earth
05:04 Temperature of Earth if there was no atmosphere
09:04 What? Find f(x)??
11:12 Differentiation Time Saver Trick
15:08 Finding f(x) with maxima
19:30 No Solution exists - so do this
23:13 Deriving Wien's Law
25:14 Peak Wavelengths of Earth and Sun
26:55 Rescaling - Hmmm
32:36 Information Overview Part B
34:24 Finding the Temperature of the Atmosphere
41:23 Finding the Temperature of the Earth with Atmosphere