Homework Questions for Chapter 19 - Light, Color, and Atmospheric Optics

Questions 1 and 2 will be turned in for a grade. Questions 3-9 will be discussed by the discussion groups in class so please look them over before the discussion session.

SHOW ALL WORK , CIRCLE THE CORRECT ANSWER, PLEASE BE NEAT AND STAPLE YOUR HOMEWORK!

ALSO, PLEASE USE A SPREADSHEET FOR ALL GRAPHS

Follow the Problem solving steps discussed in class

1. Air molecules have sizes of D = 0.0001 to 0.001 micrometers, which are much smaller than the wavelengths of visible light (l = 0.4 - 0.7 micrometers). The air molecules, therefore, cause Rayleigh scattering. The ratio of scattered intensity of radiation I_scat to the incident radiation intensity I_o is given by:

where a = 1.59x10^-23 kg, r is the air density, n_air is the refractive index, and x is the path length traveled through the air by the light. The refractive index of a particular wavelength of radiation is defined as C_o/C_air where C_o is the speed of the light in a vacuum (3x10⁸ m/s) and C_air is the speed of the light in air.

Make a plot of I_scat/I_o for violet light (l=0.4 micrometers) versus distance. Beyond approximately what distance will you likely not see a violet object? Assume that r = 1 kg m^-3 and n = 1.0002817.

2. As discussed in class, mirages form as light passes through layers of air having different densities. A ray of light will be bent upward when warm air is found below cold air, forming an inferior mirage. The radius of curvature for the ray path (positive for concave up) is given by:

where T is temperature, P is pressure, T_STP = 15ºC, P_STP = 1013.25 hPa, a = 0.0342 K m^-1, a is the angle of the ray above horizontal, and n_nsp > 1.

a. At least how quickly must the temperature decrease with height to produce an inferior mirage. Note that for an inferior mirage, the ray path must bend upward, or R_c > 0.

b. Provide a real-world example of where such a lapse rate would be observed.

3. Explain why on a cloudless day the sky will usually appear milky white before it rains and a deep blue after it rains.

4. How long does twilight last on the moon?

5. Why is it often difficult to see the road while driving on a foggy night with your high beam lights on?

6. What would be the color of the sky if air molecules scattered the longest wavelengths of visible light and passed the shorter wavelengths straight through? Explain your answer with the aid of a diagram.

7. If there were no atmosphere surrounding the earth, what color would the sky be at sunrise? At sunset? What color would the sun be at noon? At sunrise? At sunset?

8. Why are rainbows seldom observed at noon?

9. Explain why smoke rising form a cigarette often appears blue, yet appear white when blown from the mouth.

10. During Ernest Shackleton's last expedition to Antarctica, on May 8, 1915, seven days after the sun had set for the winter, he saw the sun reappear. Explain how this event called the Novaya Zemlya effect can occur.