EXPONENTIAL AND LOGARITHMIC FUNCTIONS

PROBLEM 3.

Sometimes different bases are used together in the same application in atmospheric work. For example, atmospheric absorption of electromagnetic radiation from the Sun and other sources is dependent on the wavelengths of the incoming radiation. Instruments carried by rockets, balloons, and satellites have shown how far in the atmosphere such radiation penetrates before being reduced by a factor of l/e, the conventional measure used in this work. The results are given in Fig. 6.1. Both the wavelength scale and the altitude scale are logarithmic, with the horizontal scale in base 10 and the vertical scale in base 2. (How much of this information could be displayed using linear scales even on a wall-sized chart?)

Fig. 6.1 shows that visible light and radio waves penetrate the atmosphere completely and reach Earth's surface. However, gases such as oxygen, ozone, nitrogen, and water vapor absorb most of the infrared, ultraviolet, X-ray, and shorter wavelengths. At what altitude will solar infrared radiation of wavelength 10^-4 m be reduced by a factor of l/e?

EXPONENTIAL GRAPHIC 3A.

EXPONENTIAL GRAPHIC 3B.

NEXT PAGE

PREVIOUS PAGE

RETURN TO SPACE MATHEMATICS HOME PAGE


INDEX

SPACE EDUCATORS' HANDBOOK HOME PAGE

SCIENCE FICTION SPACE TECHNOLOGY HOME PAGE

SPACE MOVIES CINEMA HOME PAGE

SPACE COMICS

SPACE CALENDAR