214
7 Light in Biology and Medicine
to show that a circularly polarized beam of light of frequency f carries a spin
angular momentum density of u/(2πf ), where u is the light energy density.
In fact, individual photons detected or emitted always have their spins aligned
or anti-aligned with the direction the light traveled. The ‘helicity’ of a particle is
the projection of its spin vector along the direction of its momentum. Relativity and
quantum theory requires that photons have helicity of ±1 ¯
h.
If all the photons had their helicities aligned in a beam of light, the light was fully
right-circularly polarized. If they were anti-aligned, the light was fully left-circularly
polarized. A coherent and equal combination of the two kinds of photons meant that
the light beam was linearly polarized. Light from the Sun and other thermal bodies is
produced with photons with a variety of frequencies and photon helicities, and little
coherence. Light detected from a laser may show billions and billions of photons
concentrated into a small set of quantum states, making the light highly coherent.
Human eyes are not sensitive to the direction of polarization. However, if you
wear polaroid glasses, you will exclude one direction of polarization in favor of
polarization perpendicular to the excluded one. 14
The scattering of sunlight by air molecules also produces partially polarized light.
You can see this by rotating your polaroid glasses in front of one eye while looking
at the blue sky in various directions. 15 Some insects can detect the direction of
polarization of light from the sky, and use this information to orient themselves.
7.4 Linear Superposition of Waves
One of the universal properties of waves of a single kind is their ability to combine
when they pass through one location at the same time. We see this as interference,
sometimes constructive, sometimes destructive. This adding of waves works for
both material (acoustical) and field waves. Waves on the surface of water make a
good visual example. We can see waves generated by stones dropped into a quiet
lake. If the stones are separated, the waves may spread from each source, combining
in the middle region. If, acting alone, the pressure in the wave from the first stone
would push the water up at some mid location, while reduced pressure in the wave
from the second stone would let the water down, the combined pressures will tend
to cancel, making destructive interference. If the two waves push the water in the
14 These glasses work by stretching long chain molecules having polar side groups parallel to one
another onto glass, as a thin layer. Visible light passing through the glass can easily vibrate the
molecules perpendicular to the chain by acting on the polar side groups, causing a loss of energy
to heat. The same light cannot so easily wiggle the chain molecules along the axis of the chains, as
the molecules are a lot stiffer in this direction. This allows waves with polarization parallel to the
molecules to pass through the glass.
15 Some ‘3-D’ glasses used in viewing 3-D films will not work seeing the polarization of the sky:
They let ‘circularly polarized’ light through, either left-circularly polarized for one eye, or rightcircularly polarized light for the other eye.
7 Light in Biology and Medicine
to show that a circularly polarized beam of light of frequency f carries a spin
angular momentum density of u/(2πf ), where u is the light energy density.
In fact, individual photons detected or emitted always have their spins aligned
or anti-aligned with the direction the light traveled. The ‘helicity’ of a particle is
the projection of its spin vector along the direction of its momentum. Relativity and
quantum theory requires that photons have helicity of ±1 ¯
h.
If all the photons had their helicities aligned in a beam of light, the light was fully
right-circularly polarized. If they were anti-aligned, the light was fully left-circularly
polarized. A coherent and equal combination of the two kinds of photons meant that
the light beam was linearly polarized. Light from the Sun and other thermal bodies is
produced with photons with a variety of frequencies and photon helicities, and little
coherence. Light detected from a laser may show billions and billions of photons
concentrated into a small set of quantum states, making the light highly coherent.
Human eyes are not sensitive to the direction of polarization. However, if you
wear polaroid glasses, you will exclude one direction of polarization in favor of
polarization perpendicular to the excluded one. 14
The scattering of sunlight by air molecules also produces partially polarized light.
You can see this by rotating your polaroid glasses in front of one eye while looking
at the blue sky in various directions. 15 Some insects can detect the direction of
polarization of light from the sky, and use this information to orient themselves.
7.4 Linear Superposition of Waves
One of the universal properties of waves of a single kind is their ability to combine
when they pass through one location at the same time. We see this as interference,
sometimes constructive, sometimes destructive. This adding of waves works for
both material (acoustical) and field waves. Waves on the surface of water make a
good visual example. We can see waves generated by stones dropped into a quiet
lake. If the stones are separated, the waves may spread from each source, combining
in the middle region. If, acting alone, the pressure in the wave from the first stone
would push the water up at some mid location, while reduced pressure in the wave
from the second stone would let the water down, the combined pressures will tend
to cancel, making destructive interference. If the two waves push the water in the
14 These glasses work by stretching long chain molecules having polar side groups parallel to one
another onto glass, as a thin layer. Visible light passing through the glass can easily vibrate the
molecules perpendicular to the chain by acting on the polar side groups, causing a loss of energy
to heat. The same light cannot so easily wiggle the chain molecules along the axis of the chains, as
the molecules are a lot stiffer in this direction. This allows waves with polarization parallel to the
molecules to pass through the glass.
15 Some ‘3-D’ glasses used in viewing 3-D films will not work seeing the polarization of the sky:
They let ‘circularly polarized’ light through, either left-circularly polarized for one eye, or rightcircularly polarized light for the other eye.