Quantum Theory of Light Wave Optics & Quantum Theory of Light

This first half of unit deals with the wave aspects of light, where only wave theory can explain the phenomena and particle/quantum theory falls short. The three primary topics of wave optics is interference, diffraction, and polarization.

Interference – Young’s Double Slit Experiment 1801 Prior to this experiment, the particle theory was the dominant view. Thomas Young devised an experiment using 2 slits to act as two point sources. What would particle theory (or rays) predict after light passed through openings onto screen?

Particle theory could NOT explain why multiple lines of light appeared on screen but wave could.

Creating a bright region directly behind barrier makes sense since light waves travel same distance, but what about other areas?

The interference occurs because each point on the screen is not the same distance from both slits.

Path length is the extra distance one of the waves travels to meet the other on the screen. This assumes that paths (d1 & d2 ) are nearly parallel and that L>>d

For Constructive Interference: A bright fringe is produced, via C. I., if the path difference is zero or some integral multiple of the wavelength where – m = 0, ±1, ± 2, …where m is called the order number • When m = 0, it is the zeroth order maximum • When m = 1, it is called the first order maximum, etc For Destructive Interference: A dark fringe is observed when the path difference equals an odd half wavelength multiple –m = 0, ± 1, ± 2,

Conditions for interference For sustained interference between two sources of light to be observed, there are two conditions which must be met – The sources must be coherent, meaning they must maintain a constant phase with respect to each other – The waves must have identical wavelengths

There is also a relationship to the location of the fringes on the screen (y) Assume L>>d where θ is small and sinθ tanθ

Intensity on screen for 2 slits Between the maxima and the minima, the interference varies smoothly.

Monochromatic light falls on two slits that are 0 Monochromatic light falls on two slits that are 0.0525mm apart producing an interference pattern on a screen 6.50m away with bright fringes that are 7.36cm apart. What is the wavelength of light?

Light with a wavelength of 650nm strikes two slits that are 7 Light with a wavelength of 650nm strikes two slits that are 7.65x10-5m apart and produce an interference pattern on a screen 4.00m away. How wide will the central fringe be that appears on the screen?

Diffraction Recall that diffraction involves waves bending around obstacles or passing through openings

Diffraction by a single slit or object Similar to 2 slits, obstacle or 1 slit causes diffraction. Slit yields same result as barrier.

We can imagine each portion of the slit as a source of waves We can imagine each portion of the slit as a source of waves. To analyze the pattern it is convenient to break slit into halves (w/2). w/2 sinθ

Could show that by dividing slit into 4 parts or 6 parts etc

Single slit pattern

How wide is a central diffraction peak on a screen 3 How wide is a central diffraction peak on a screen 3.60m behind a slit, with a width of 0.0344 mm, when illuminated by 440nm light?

Multiple slits produce an array of colors (diffraction grating) depending on the angle you view the ‘screen’. White light reflected from closely spaced grooves in CD causes constructive interference in certain directions for different colors. Iridescence of peacock feathers is caused by light reflected from complex layered surface. Different colors of white light interfere at different locations.

Thin Films

Essentially, part of an incident wave is reflected off the top surface of film while the other part is transmitted into the thin film where it reflects off bottom surface (of film). Waves are NEARLY parallel.

Relating wavelength to index of refraction When light enters new medium, v and λ both change Note that lambda sub zero is either monochromatic incident light (where color won’t change after reflection) or you will have incident white light where lambda sub zero is the reflected light you end up seeing

Not only can reflection cause a phase shift so that waves are out of step, but so can the distance traveled in the film itself.

Thickness of Soap Bubble Skin What is minimum thickness t of soap bubble if it appears green (l=540 nm) at the point of front surface closest to viewer? Assume nsoap = 1.35.

Example2 Light (λ=550nm) moves from air to a film of silicon oxide which sits on silicon. What minimum thickness of film must be present to get zero reflection?

A similar effect takes place when a shallowly curved piece of glass is placed on a flat one. When viewed from above, concentric circles appear that are called Newton’s rings.

Example: Two long, flat pieces of glass plates are placed one on top of the other separated only by a thin piece of plastic at one end. Side view If there are 37 dark and 37 bright lines starting from the end of the pair of glass plates that are touching to the other, how thick is the piece of plastic when illuminated by a sodium lamp (λ=589nm)?

How a laser ‘reads’ a CD

Polarization (only light waves) Light waves oscillate in all planes coming from a source. Sunlight is considered to be unpolarized. Polarized light oscillates in one particular plane. When light reflects off surface, it polarizes in that plane.

Polarized Filters Polarized filters only allow one plane of light to pass through, similar to a picket fence. A vertical polarizer will only allow vertically polarized light to pass.

This means that if initially unpolarized light passes through crossed polarizers, no light will get through the second one.

Sunglasses

Structural Analysis CD case In industry, Polaroid filters are used to perform stress analysis tests on transparent plastics. As light passes through a plastic, each color of visible light is polarized with its own orientation. If such a plastic is placed between two polarizing plates, a colorful pattern is revealed. As the top plate is turned, the color pattern changes as new colors become blocked and the formerly blocked colors are transmitted. It is known that structural stress in plastic is signified at locations where there is a large concentration of colored bands. This location of stress is usually the location where structural failure will most likely occur. CD case Show ruler between 2 filters on overhead, flat and then bent, to show stress

3-D MOVIES Polarization is also used in the entertainment industry to produce and show 3-D movies. Three-dimensional movies are actually two movies being shown at the same time through two projectors. The two movies are filmed from two slightly different camera locations. Each individual movie is then projected from different sides of the audience onto a metal screen. The movies are projected through a polarizing filter. The polarizing filter used for the projector on the left may have its polarization axis aligned horizontally while the polarizing filter used for the projector on the right would have its polarization axis aligned vertically. Consequently, there are two slightly different movies being projected onto a screen. Each movie is cast by light which is polarized with an orientation perpendicular to the other movie. The audience then wears glasses which have two Polaroid filters. Each filter has a different polarization axis - one is horizontal and the other is vertical. The result of this arrangement of projectors and filters is that the left eye sees the movie which is projected from the right projector while the right eye sees the movie which is projected from the left projector. This gives the viewer a perception of depth.