Physical or wave optics

Transcription

1 Physical or wave optics In the last chapter, we have been studying geometric optics u light moves in straight lines u can summarize everything by indicating direction of light using a ray u light behaves essentially the way a stream of particles (photons) would This has worked well for a number of phenomena u reflection u refraction and has helped us to understand the workings of u mirrors u thin lenses But our particle theory of light gives out when we try to understand phenomena like interference, diffraction and polarization u just doesn t work Have to resort to wave or physical optics (in this chapter) u and treat light like a wave The first thing we ll look at is interference of light waves u not easy to observe because of the short wavelengths of light involved (4X10-7 m to 7X10-7 m) Along the way we ve going to find out why the sky is blue

2 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

3 Young s Experiment In order to observe interference of 2 light waves, need to have 2 things present u sources must be coherent (same phase with respect u to each other) waves must have identical wavelength Laser produces coherent light which can be split into two light beam which then can interfere with each other But the first interference experiment was carried out in 1801 u no lasers then

4 Young s Experiment In order to observe interference of 2 light waves, need to have 2 things present u sources must be coherent (same phase with respect u to each other) waves must have identical wavelength Laser produces coherent light which can be split into two light beam which then can interfere with each other But the first interference experiment was carried out in 1801 u no lasers then Sunlight shines through a narrow slit; the light then spreads (Huygen s principle) and illuminates a second screen with 2 small slits The waves through S 1 and S 2 spread out and interfere with each other producing a series of bright and dark fringes

5 Interference fringes

6 Wrong! Huygen s principle

7 Remember example

8 Constructive interference When light arrives from S 1 and S 2 so that constructive interference takes place, a bright fringe results

9 Destructive interference If the light arrives from S 1 and S 2 at a point on the screen and there is destructive interference, then there is a dark spot

10 Interference patterns 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 if d sin q is a multiple of the wavelength l, then constructive interference occurs d sin q = ml m=0,+/-1, +/-2,

11 Interference patterns 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 dark = (ll/d)(m+1/2) if d sin q is an odd multiple of the wavelength l/2, then destructive interference occurs d sin q = (m+1/2)l m=0,+/-1, +/-2,

12 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 if d sin q is an even multiple of the wavelength l, then constructive interference occurs d sin q = ml m=0,+/-1, +/-2,

13 Thin film interference Interference can also be observed in other situations (in fact, I guarantee it has been by you) such as thin films But before we talk about thin films, we have to talk about phase changes when waves reflect at an interface For example, when a light wave reflects from a surface that has a higher index of refraction, there is a phase shift of 180 o

14 But when a light wave reflects from a surface that has a lower index of refraction, there is no phase shift Thin film interference

15 Reflections from a thin film Part of the wave reflects from the top surface and part from the bottom surface The part that reflects from the top surface has a 180 o phase change while the part that reflects from the bottom does not When will there be constructive interference between the two reflected waves?

16 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

17 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

18 As for example non-reflective coating for a solar cell

19 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