Corrections indicated below for Problem 6.
Updated to include constants necessary to compute some of the problems.

    Solve the problems below using the equations and concepts discussed in class.  Include units with all the answers and discussion were appropriate.

1.  The meter (m) is the basic unit in which wavelengths are measured.  Convert 0.5 micrometers to its equivalent frequency.  Also convert 33GHz (common unit of measure in the microwave portion of EMR) to wavelength (in meters and micrometers).

2. Calculate the total radiant exitance from the sun assuming it is a 6000K blackbody. Also, determine the wavelength of maximum emission (in micrometers). This corresponds with what wavelength of light.

 
3. Compute the total radiant exitance from a blackbody with a temperature of 300K.  Determine the wavelength of maximum emission (in micrometers).  This corresponds with which wavelength region?  Discuss importance in relation to the Earth as a blackbody.

4. The radiant flux from the sun is 3.9x10²⁶ W. Calculate the solar constant (Wm^-2). The solar constant is the flux per square meter of solar radiation at the outer boundary of the Earth's atmosphere that is received on the surface held perpendicular to sun's rays, averaged over the year.

5. Suppose that the sun were somewhat bluer in color, so that its wavelength of maximum irradiance were 0.400 micrometers instead of 0.475 micrometers. Estimate the radiative equilibrium temperature of the earth under these conditions, assuming the albedo remains the same.

6.  A body is emitting radiation in the following idealized spectrum of monochromatic radiation:

lambda < 0.35 um,  E_lambda = 0

0.35 um < lambda < 0.50 um,  E_lambda = 1.0 Wm^-2 um^-1

0.50 um < lambda < 0.70um,  E_lambda = 0.5 Wm^-2 um^-1

0.70 um < lambda < 1.00 um,   E_lambda = 0.2 Wm^-2 um^-1

lambda > 1.00 um,  E_lambda = 0

            Compute the irradiance.

 
7. 150 Wm^-2 of direct 'red' solar radiant flux irradiates a soil surface with a 'red' absorptance of 0.80. How much energy is reflected from the surface?

8. On a hazy day, what type of scattering dominates. Explain.

9. Explain why the sky appears brilliant colors of orange and red during some sunsets.

10. You are a geologist looking at finding particular mineral resources associated with oil and gas reserves using satellite data. The mineral resources are spectrally sensitive in the ultraviolet through mid-infrared region of the spectrum. What portions of this region would be most beneficial for your investigation?

Constants

 

speed of light (c) = 2.99792458 x 10⁸m s^-1

Stefan-Boltzman's constant  (sigma) = 5.67051 x 10^-8 m^-2 K^-4

mean Sun-Earth distance (d_se) =1.4956 x 10¹¹ m

radius of Sun (r_s) = 6.9595 x 10⁸ m

radius of Earth (r_e) = 6.371009 x 10⁶ m

Due on Friday, October 1, 1999.

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Last revised on September 23, 1999 by Tracy DeLiberty.