218
7 Light in Biology and Medicine
The color of oceans and lakes combines the colors reflected from the sky with the
color of material in the water at its surface.
Scattering from large spheres (Mie scattering) is, for the same reason, also
frequency independent. A good example is light scattered from large water droplets,
such as in clouds. Small particles in the air, such as fine smoke, in contrast, will
have a blue shade. This is a case in which the particle diameter is comparable to the
wavelength of the light being scattered.
7.7 Dispersion of Waves in Media
Light, even when it seems to pass straight through a transparent material, such as the
protoplasm of a cell, is nonetheless affected by the charges in the material. Charges
jiggle in the material in response to the passing wave. If their jiggling has a natural
vibrational frequency matching that of the passing light frequency, resonance will
occur. The oscillating charges will radiate light, causing some light scattering. In
effect, a fraction of the light passing by is absorbed and then re-radiated by those
charges. Since there is a time delay between absorption and re-radiation, the light
wavelets generated by the material charges will be out of phase with the light passing
by, with the phase of the wavelets shifted back from the originating light. Adding
the scattered light to the light passing by unscattered gives the resultant wave. The
sequential phase shifts causes the resultant wave to be delayed, and the light takes a
greater time to reach the other side of the material than it would have taken across
a vacuum. This is why the speed of light in glass, or in the vitreous humor of your
eye, 17 is less that in a vacuum.
The ratio of the speed of light in a vacuum to the speed in the materials is
called the ‘index of refraction, n’ of the material: n = c/v. Because the resonances
of charges in the material occur at different frequencies, the index of refraction
may have a complicated frequency dependence. Water (and therefore many dilute
organic solutions) has ultraviolet resonances due to electron motions and infrared
resonances due to molecular vibrations. Together, these resonances make the index
of refraction for water rise as a function of frequency in the visible part of the
spectrum. The same is true of glass, and many other transparent crystals. So, blue
light in water and glass will be slowed more than red.
The behavior of the index of refraction for varying frequencies, n = n(f ), is
called a ‘dispersion relation’, because this variation makes glass prisms disperse
white light into its component rainbow colors (with blue bent to a greater angle than
red, being that blue is a higher frequency, and is close to the UV resonances).
17 Some light-headed people may be slowed by vicious humor, but that’s a different story.
7 Light in Biology and Medicine
The color of oceans and lakes combines the colors reflected from the sky with the
color of material in the water at its surface.
Scattering from large spheres (Mie scattering) is, for the same reason, also
frequency independent. A good example is light scattered from large water droplets,
such as in clouds. Small particles in the air, such as fine smoke, in contrast, will
have a blue shade. This is a case in which the particle diameter is comparable to the
wavelength of the light being scattered.
7.7 Dispersion of Waves in Media
Light, even when it seems to pass straight through a transparent material, such as the
protoplasm of a cell, is nonetheless affected by the charges in the material. Charges
jiggle in the material in response to the passing wave. If their jiggling has a natural
vibrational frequency matching that of the passing light frequency, resonance will
occur. The oscillating charges will radiate light, causing some light scattering. In
effect, a fraction of the light passing by is absorbed and then re-radiated by those
charges. Since there is a time delay between absorption and re-radiation, the light
wavelets generated by the material charges will be out of phase with the light passing
by, with the phase of the wavelets shifted back from the originating light. Adding
the scattered light to the light passing by unscattered gives the resultant wave. The
sequential phase shifts causes the resultant wave to be delayed, and the light takes a
greater time to reach the other side of the material than it would have taken across
a vacuum. This is why the speed of light in glass, or in the vitreous humor of your
eye, 17 is less that in a vacuum.
The ratio of the speed of light in a vacuum to the speed in the materials is
called the ‘index of refraction, n’ of the material: n = c/v. Because the resonances
of charges in the material occur at different frequencies, the index of refraction
may have a complicated frequency dependence. Water (and therefore many dilute
organic solutions) has ultraviolet resonances due to electron motions and infrared
resonances due to molecular vibrations. Together, these resonances make the index
of refraction for water rise as a function of frequency in the visible part of the
spectrum. The same is true of glass, and many other transparent crystals. So, blue
light in water and glass will be slowed more than red.
The behavior of the index of refraction for varying frequencies, n = n(f ), is
called a ‘dispersion relation’, because this variation makes glass prisms disperse
white light into its component rainbow colors (with blue bent to a greater angle than
red, being that blue is a higher frequency, and is close to the UV resonances).
17 Some light-headed people may be slowed by vicious humor, but that’s a different story.