Electromagnetic waves Now we re back to thinking of light as specifically being an electromagnetic wave u u u oscillating electric and magnetic fields perpendicular to each other propagating through space equal amounts of energy stored in the electric field and in the magnetic field in interactions with matter, it s the electric component that does most of the work
Example Light from slit S 2 has to travel further then light from S 1 path length difference is d sin q y = L tan q > L sin q y bright = (ll/d)m m=0 if d sin q is an even multiple of the wavelength l, then constructive interference occurs d sin q = ml m=0,+/-1, +/-2, m=-1 m=0 m=1 m=2
Example Light from slit S 2 has to travel further then light from S 1 path length difference is d sin q y = L tan q > L sin q y bright = (ll/d)(m+1/2) if d sin q is an odd multiple of the l/2, then destructive interference occurs d sin q = (m+1/2)l m=0,+/-1, +/-2, m=-1 m=0 m=1 m=2
Reflections from a thin film Wave #2 has to travel further by a distance 2t (ignore any angle) So you might think that if 2t = ml(where m is an integer) that you would get constructive interference But ahh the phase shift so I get constructive interference when 2t = (m+1/2)l But ahh I remember that the wavelength changes inside the film to l n =l/n so, finally, I get constructive interference when u 2t = (m+1/2) l n u or 2nt = (m+1/2)l
Reflections from a thin film So I get destructive interference when u 2t = m l n u or 2nt = ml Two things influence whether I have constructive or destructive interference (or somewhere in between) u difference in path length travelled u any phase changes on reflection s in this example, I have one 180 o phase shift because I m going from air to a film with an index n back to air If this was a material with an index > n, then I d have a 2nd 180 o phase shift
As for example Constructive interference when 2nt = ml Destructive interference when 2nt = (m+1/2)l non-reflective coating for a solar cell
What happens when I have a wedge-shaped film have constructive interference when 2nt =(m+1/2)l Note that bands of color show up whenever the thickness leads to constructive interference for that color
Diffraction no yes
Diffraction Diffraction occurs when a wave passes through a small opening not so different in size from the wavelength of the wave The wave spreads out as we saw on the previous slide So instead of a bright spot just in the middle we see a spread-out distribution of light u but with some structure to it Type of diffraction we re studying is called Fraunhofer diffraction u screen is far away from slit u or there s a converging lens just after the slit u Demo Don t worry about the lens; Just think of the screen as far away
Where are the dark spots? Here s where Huygen s principle comes in handy As the wave travels through the slit, treat each point in the slit as a source of waves Light from one part of the slit can interfere with light from another part Let s divide the slit into halves and consider the wavelets coming from point 1 and from point 3 Wavelet 1 has to travel further IF the additional distance, a/2sinq is equal to l/2, then the wavelets from points 1 and 3 are exactly half of a wavelength out of phase u destructive interference Also true for 3 and 5, 2 and 4, any two points in the top and bottom of the slit separated by a/2 Can go through the same exercise dividing the screen in 4 parts, 6 parts,
Dark spots So dark spots when u a/2 sinq = l/2 u or a/2 sinq = 2l/2 u or a/2 sinq = 3l/2 Corresponding to u u u u sinq 1 = l/a sinq 2 = 2l/a sinq 3 = 3l/a Everything is in phase at q=0, so there s a bright spot there u and other bright spots roughly half-way between the dark spots
Back to 2 slits When I shine coherent light through two narrow slits, I see BOTH diffraction and interference I see the overall diffraction pattern with the interference fringes inside Back to demo
Let s go crazy and put in lots of slits Light diffracts through each of the slits A device like this is called a diffraction grating but there s both diffraction and interference taking place and we get interference between each of the diffracted waves Again, there s a path length difference between light passing through different slits bright lines or spots when d sinq bright = ml m=0,1,2,
Intensity pattern The more slits in the grating the sharper are the interference peaks; Can also make a diffraction grating by having finely etched lines on a reflective surface
Polarization of electromagnetic waves Remember our picture of light as an EM wave; oscillating electric and magnetic fields Here I ve drawn the E field as oscillating along the y-axis but could be any orientation (but transverse to direction of propagation) The orientation of the E-field in the wave is called the polarization of the wave; for light, polarization is transverse
Polarizing filters Polaroid material consists of long hydrocarbon chains which conduct only along the direction of the chains So they absorb light whose electric field vector is parallel to their chains and transmit light whose electric field is perpendicular I=I o cos 2 q
Example Transmission through filters changes as relative orientation changes.
Polarization by reflection When unpolarized light is reflected from a surface, it can become partially (or even completely) polarized Portion of the EM wave that has polarization parallel to the surface reflects more strongly than does portion which has polarization perpendicular to surface u so reflected light ends up partially polarized
At one particular angle (when reflected and transmitted waves form an angle of 90 o with respect to each other), the reflected light is 100% polarized Brewster s angle (after Sir David Brewster) q p u tan q p = n Brewster s angle going from air to a medium of index n
Polarization by scattering (what you ve all been waiting for) When light passes through the earth s atmosphere, the electrons in the gas atoms can absorb and re-emit the light u this is called scattering and is why the sky is not black in the daytime The air molecules act like an antenna when they re-radiate the EM waves u if the EM polarization of the incident wave is parallel to the Earth s surface, the antenna radiates an EM wave downward with the same polarization so sunlight is not polarized but the light from the sky is
But why is the sky blue? Sunlight has all visible wavelength components (but peaks in yellow) High frequency components of sunlight scatter more readily from the air molecules than low frequency components So we see those high frequency components, i.e. blue light, when looking away from the sun
What color is the moon s sky? Other examples What color is sky on Mars? What color is the sunset on Earth?