2013
The Sun through London fog
- Round
- Theory
- Points
- 10
- Level
- Bronze
- Taught in
- Section 4.4
Adapted from IOAA 2013 (Volos), theory problem S13. We have restated it in our own words and kept the original data, adding the magnitudes of the Sun and the full Moon. The solution was last checked on 20 October 2026.
On a day of very thick fog in London, the Sun looked only as bright as the full Moon usually does on a clear night. Assume that the fog dims light exponentially, and find the optical depth of the fog. Take the magnitude of the Sun as −26.74 and that of the full Moon as −12.74.
Find how many magnitudes the fog took away, then turn magnitudes into an optical depth.
- The fog dimmed the Sun by
- By (4.6),
- The fog let through only
AnswerThe fog had an optical depth of about 12.9.
This problem also appears among the olympiad problems of Section 4.4, Extinction, airmass and optical depth, which teaches the ideas it uses. Equation and figure numbers refer to the course.