Chapter 15.1 Sunlight
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#14	#22	#28

2. How long should an antenna be to receive or transmit violet light well?

An antenna works particularly well when it is about one-fourth the size of the electromagnetic wave it is designed for. Since violet light has a wavelength of around 420 nm, the antenna should be about 105 nm long.





6. Although we can't see them, Rayleigh scattering also occurs for infrared and ultraviolet light. Which of these two types of light experiences the strongest Rayleigh scattering?

We know that the sky appears blue because the Rayleigh scattering of blue light is stronger than that of red light, even though blue light is not scattered very effectively. This happens because red light is scattered even less than blue. Infrared light undergoes weaker Rayleigh scattering than red light, while ultraviolet is scattered more strongly than blue because the wavelength is becoming a better match to the size of the molecules. So ultraviolet light experiences stronger Rayleigh scattering than infrared.





8. When astronauts walked on the surface of the moon, they could see the stars even though the sun was overhead. Why can't we see the stars while the sun is overhead?

On the moon, there is no atmosphere with dust particles to scatter incident sunlight in random directions. Thus, the sky appears black even when the sun is overhead.

On the earth, our atmosphere (with its complement of dust and pollen) strongly scatters the incident sunlight in all directions. This causes the blue glow of our sky during the day, as well as other scattering of light. This general background of scattered light makes our sky appear bright during the day, obscuring our view of any other light source that is not as bright as the scattered sunlight. The stars are not bright enough to be seen during typical daylight.





14. Why can you see your reflection in a calm pool of water?

Light that is traveling in air must slow down as it begins to enter water with its higher refractive index. The process of slowing down causes some of it to reflect instead of continuing into the water. If the water is calm and even, the reflected light returns like it does from a mirror.





22. Diamond has an index of refraction of 2.42. If you put a diamond in water, you see reflections from its surfaces. But if you put it in a liquid with an index of refraction of 2.42, the diamond is invisible. Why is it invisible and how is this effect useful to a jeweler or gemologist?

Light reflects from the diamond's surfaces in water because light entering the diamond from water must slow due to the diamond's higher index of refraction. Some light will also reflect upon exiting from the diamond into water since the light must speed up for water's lower index of refraction. When the diamond is in a liquid with an index of refraction of 2.42, the light does not speed up or slow down when it enters or exits the diamond, and there is no reflection produced at these surfaces.

This effect could be useful to verify that an object is a diamond by checking its index of refraction. It would also permit the jeweler to examine the interior of the diamond for flaws, without being hampered by extraneous reflections from the diamond's facets.





28. Why is it easier to see into water when you look directly down into it than when you look into it at a shallow angle?

When we look into water, we see things underneath the water by the light that comes from them to our eyes. This light exits from the higher refractive index of water to the lower refractive index of air before it reaches us. When it does so, the light rays speed up as they exit the water and refract to an angle further from the vertical than they had while in the water. At the same time, some of the light reflects back into the water rather than emerging into the air.

If the light rays' underwater angle (with respect to the vertical) is large enough, the exiting light rays refract so that they just skim along the boundary between water and air. At any greater underwater angle, they completely reflect back into the water and do not emerge into air. This is called "total internal reflection" and the limiting angle for light no longer able to emerge from the water into air is the "critical angle." Going from water into air, the critical angle is about 49 degrees.