Wave Optics

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

A bright fringe is produced, via C. I., if the path difference is zero or some integral multiple of the wavelength where

A dark fringe is observed when the path difference equals an odd half wavelength multiple–m = 0, ± 1, ± 2,

For Constructive Interference:

– 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:

Conditions for interferenceFor sustained interference between twosources of light to be observed, there aretwo conditions which must be met– The sources must be coherent, meaning they must maintain a constant phase with respectto 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 0.0525mm 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?

Diffraction

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

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

Single Slit Diffraction explained

How does a single slit produce a series of bands like double slit?

Consider a slit of width, w. As a wave front approaches, imagine each portion of the slit as a source of waves.

If we consider the rays that travel northeast through the slit towards a screen. Note that rays aren’t parallel.

If we look at ray 5 (just below edge of slit) and ray 3 (center of slit),

In fact, another ray just below ray 5 and just below 3 will also cancel

Single slit pattern

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?

Iridescence of peacock feathers is caused bylight reflected from complex layered surface. Different colors of white light interfere at different locations.

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.

Resolution of single slit and circular apertures

The ability of a lens to produce distinct images of 2 point objects very close together is called resolution. The closer the 2 objects can be seen as distinct, the higher the resolution.

Because of diffraction, there is a limit on the resolution by optical devices such as your eye or a telescope.

Resolving Power

How close can two points of light be to still be resolved as 2 distinct light points instead of one?

Two sources of light are just resolvable when the

S2

S1

θ

2 sources far apart

2 sources are close enough together that they are ‘just resolved’

2 sources so close that they are not resolved

A motorcycle has twin headlights which emit light with an average wavelength of 550nm. The diameter of the pupil is 4.3mm, at what distance can the two headlights be resolved if the headlights are a distance 20cm apart?

The camera on a spy satellite has a lens with a diameter of 1.5m. This satellite is in low earth orbit about 2.9x105m above the surface of the Earth.  Determine the approximate size of the smallest feature the camera can resolve when taking a picture of something on the Earth's surface (assume blue light with a λ = 400nm, and ignore the effect of the Earth's atmosphere)

Is it easier to resolve two headlights during the night or day?

Hint: What is the difference with your pupils during the day vs the night?

Application: The Eye Chart and 20/20 vision

The chart is based on a standard distance of 6.0m or 20 feet.20/20 vision means you can distinguish the letters on the fourth line up (8) from the bottom at a distance of 20ft.

The basic scheme is that the letters two rows down are half the size, and two rows up twice the size, etc

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

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.

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

Thickness of Soap Bubble Skin

Example2Light (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 atone end.

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)?

Side view

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