CH. 24Wave Optics

The sources must be “coherent”. This means they emit waves with a constant phase with respect to each other.

The waves need to have identical wavelengths. Can’t be coherent without this.

Incoherent – When the phase between the two waves is not constant.

Here is a relatively easy way to produce coherent light sources:

Pass monochromatic light (light with only 1 wavelength) through a slit.

Light passes through the single slit, exiting as a single wave front that reaches two more slits at the same time. These two slits are equally spaced from the first.

The second pair of slits will then act as a pair of coherent light sources.

Figure 24.1

Experiment used to observed interference pattern from light emerging from two slits (pinholes).

Observe alternating bright and dark parallel bands (fringes).

The bright bands show constructive interference.The dark bands show destructive interference.

Constructive interference occurs where the light from the two slits, hits the screen in phase.

Destructive interference occurs where the light from the two slits, hits the screen out of phase.

θbright corresponds to the angle to the bright fringes.

The central bright fringe occurs when m = 0.This is called the zeroeth-order maximum.

To simplify our math, we can make the assumption that L >> d. The distance (L) to the screen is much larger than the slit separation (d).

Also we assume that d >> λ. The slit separation (d) is much larger than the wavelength (λ).

Using the previous assumptions, means θbright and θdarkwill be small angles.Useful assumption: For small angles sin𝜃𝜃 ≈ 𝜃𝜃: sin θ is approximately θ.

Changes in phase due to reflectionWhen light reflects off of a medium that has a higher index of refraction than the initial medium’s index of refraction, the electromagnetic wave undergoes a phase change of 1800.

If n1 < n2: there is a phase change from reflection.If n1 > n2: there is no phase change from reflection.

Figure 24.6, 24.7

In figure 24.7, the two reflected beams interfere with each other.Assume “nearly normal incidence angles”.

Due to this change of phase from reflection, we can use thin films, or coatings, to produce an interference pattern.

We will need to use the relationship that the wavelength in a medium with index of refraction “n” is: λn = λ/n .

Let Ray 1 be the reflected ray from the top surface of the film. Its phase changes by 1800. This is equivalent to having a path difference of λ/2.

Ray 2 passes through the film and reflects off the bottom surface before coming back out the top.

If the thickness of the film is “t”, the extra distance traveled by Ray 2 is 2t.

Due to this change of phase from reflection, we can use thin films, or coatings, to produce an interference pattern.

Examples:Soap bubble Antireflective coatings for opticsThin layer of water on ice surfaceCoatings used to reduce radar signature of stealth aircraft

Example of light incident on a thin film in air where the index of refraction of the film is greater than n = 1 for air.

Let ray 1 be reflected from the top surface of the film. The index of refraction goes from small to big, so the phase changes by 1800. This is equivalent to a path difference of λ/2.

At the bottom boundary, the light goes from the film to air, so index of refraction goes from bigger to smaller. So there is no phase change. Ray 2 passes through the film and some of it reflects off the bottom surface before coming back out the top, so it travels an extra distance of twice the film’s thickness.

Ray 1 changes its phase by 1800. This is equivalent to a path difference of λ/2

Ray 2 does not have the phase change…… but the light traveled an extra distance of twice the thickness (2t).

If the extra distance traveled by Ray 2 is an odd multiple of λn/2, the two waves recombine in phase and constructive interference occurs.

Destructive interference in a thin film happens when the extra distance traveled by Ray 2 is an integer multiple of λn.

2t = mλn and use substitution λn = λ/nFor destructive interference in a thin film:

2nt = mλ m = 0, 1, 2, 3, ...

See page 843 for “Thin film interference strategies”Note the dependence on the number of phase reversals

This chart is a big deal.See examples 24.2, 24.3

Diffraction

When a wave front passes through a small space or around a sharp edge, the shape of the wave front changes.

For example when plane waves pass through a thin slit, spherical waves come out.

Fig. 24.13 shows the light waves passing through a pair of narrow slits.Fig 24.4 shows the diffraction pattern of a single narrow slit.

Can be observed in 1-D or 2-D.Fig 24.5 shows the diffraction pattern of a pinhole.

Figure 24.18 shows the interference pattern from single slit diffraction.

When light passes through a slit, we can treat the different parts of the slit as multiple sources of light. The light from the different portions of the slit will interfere with each other.

All the light at the slit is in phase. Notice that in figure 24.17, some of the rays have to travel farther than others to reach the locations on the screen.

Diffraction gratingA diffraction grating is a tool that can be used to analyze light sources.

A diffraction grating consists of a large number of equally spaced parallel slits.

A cheap way to make one is to scratch parallel lines on a glass plate. The scratches are not clear like the rest of the glass. So the gaps between scratches (where the glass is still clear) act as the slits.

The gaps and the scratches need to be small, because the wavelength of light is small. A typical grating has several thousand lines per centimeter. It would be very tedious to make one by hand.

Light is a wave. We call these, electromagnetic waves.

The concept of polarization is good evidence that electromagnetic waves are transverse.

Electromagnetic waves consist of oscillating electric and magnetic fields, that are oriented at 90 degrees to each other. Both field oscillate perpendicularly to the direction of wave motion.

See figure 24.24

As a convention, we choose the polarization to correspond to the orientation of the electric field.

When charges vibrate, they act like tiny antennae that radiate electromagnetic radiation. The electric field will oscillate in the direction of the vibration.

Because vibrations can occur in all directions, the resultant electromagnetic wave is a superposition of all the waves produced by the vibrating charges.

This results in unpolarized light. There are waves with the electric field oscillating in all directions.

If the electric field vibrates in the same direction every time, linearly polarized light is produced. The electric field oscillates in just one direction.

See figure 24.25We can produce this by applying an AC voltage to a linear antenna.

Polarizer = Device that produces polarized light by the selective absorption of any non-aligned electromagnetic waves using linearly aligned molecules. (Molecules are oriented parallel to each other and are “long” in one dimension.)

The molecules absorb any light whose electric field component is parallel to the molecules. They transmit light that has an electric field perpendicular to their long dimension.

The direction that is perpendicular to their long dimension is called the transmission axis.

By absorbing any perpendicularly oriented light, polarizing light reduces the intensity of the light that passes through the polarizer, if any of the light is not aligned along the transmission axis.

When unpolarized light passes through any polarizer, half the intensity is transmitted.

If a second polarizer is used, the second is called an analyzer, the transmitted beam’s intensity is reduced depending on the angle between the polarizers.

All the light is blocked when two consecutive polarizers have their transmission axis at 900 angles apart.

Note that if there are more than two polarizers, you need to pay attention to the orientation of them all.Most importantly, what are the relative angles of each adjacent pair of polarizers?!?!Here we have unpolarized light incident on two sets of three identical polarizers. Two very different results!!!

A common application of the polarization and/or polarizers is polarized sunglasses.When sunlight reflects off of a body of water, the reflection or “glare” is polarized. Cheap sunglasses merely make everything darker. Polarized sun glasses eliminate the glare by absorbing the polarized reflected light.

Good for being out on the lake.Bad for skiing down a slope where there are icy patches.

Polarized filter for cameras.Makes the image the camera sees more vibrant.