unit 12: part 1 physical optics: the wave nature of light

Unit 12: Part 1Physical Optics: The Wave

Nature of Light

Overview

Young’s Double-Slit Experiment

Thin-Film Interference

Diffraction

Polarization

Atmospheric Scattering of Light

Young’s Double-Slit Experiment

Passing a beam of light through a pair of slits produces two beams that are in phase, and can interfere with each other.

Young’s Double-Slit Experiment

Whether the interference is constructive or destructive depends on the path length difference from the slits to the screen.

Young’s Double-Slit ExperimentThe condition for constructive interference:

Young’s Double-Slit Experiment

The condition for the location of an interference maximum is then

Here, n is called the order of the maximum.

The lateral distance between maxima is, for small angles,

Thin-Film Interference

If light reflects from a medium of higher index of refraction, there is a 180° phase shift. If it reflects from a medium of lower index of refraction, there is no phase shift.

Thin-Film InterferenceThe colors of an oil spill come from interference of waves reflecting from the surface and from the oil–water interface.

Thin-Film Interference

In determining whether the interference will be constructive or destructive, we must take into account not only the path length difference, but also whether or not the phase shifts on reflection, and the fact that the wavelength is shorter in the film than it is in the air.

Constructive interference occurs when the thickness of the film is given by:

Thin-Film Interference

Thin-film interference is also useful for determining the flatness of a reflecting surface.

If the surface is not flat, the bands will not be straight and even.

Thin-Film Interference

A similar technique can be used to check lenses. If the lens is not shaped properly, the bands will be distorted.

DiffractionDiffraction patterns are created when waves encounter obstacles or openings, or are very close to the edges of objects.

DiffractionAgain, path length differences from different parts of the object or opening lead to interference.

The condition for diffraction minima is:

The diffraction pattern will be wider for longer wavelengths and narrower slits.

The central maximum is twice as wide as the side maxima; its width is:

Diffraction

A diffraction grating is a series of small slits with uniform spacing. The maxima become quite narrow.

DiffractionDiffraction gratings combine multiple-slit interference with single-slit diffraction, yielding the observed pattern.

Diffraction

The maxima of a diffraction grating are the same as for a double slit:

If the light falling on a diffraction grating is not monochromatic, a spectrum will be seen, as different wavelengths will have peaks at different places. A familiar example of a (reflection) diffraction grating is a CD.

Diffraction

Most spectroscopy is now done with diffraction gratings rather than prisms.

Diffraction

The wavelengths of X-rays are such that they can be diffracted by crystal planes—the spacing between planes of atoms is roughly the same as the wavelength of X-rays.

Again, for constructive interference,

DiffractionX-ray diffraction is now used to determine crystal structure.

Polarization

Polarization refers to the orientation of the electric and magnetic fields in an electromagnetic wave.

Polarization

In unpolarized light, the electric fields have random directions.

In partially polarized light, the electric fields are clustered around a preferred orientation.

In fully polarized light, the electric fields are all in the same direction.

Polarization

Some crystals preferentially absorb light of a particular orientation. If light passes through a sufficiently thick crystal, it will be polarized when it exits.

Polarization

Sheets of polarizing material transmit light of only one polarization. If such sheets are placed at right angles to each other, no light is transmitted.

Polarization

If polarizing sheets are placed at an angle other than 0° or 90°, the transmitted intensity is given by Malus’s law:

PolarizationLight is partially polarized upon reflection and refraction. For a particular angle, called Brewster’s angle, the reflected light is completely polarized.

Polarization

Brewster’s angle, also called the polarization angle, is given by:

PolarizationLight reflecting from horizontal surfaces is partially polarized in the horizontal direction. Vertically polarized sunglasses can reduce the “glare” considerably.

Polarization

Some crystalline materials have indices of refraction that are different along different planes. These materials are called birefringent.

Here, the two rays are polarized differently.

PolarizationSome materials are able to rotate the plane of polarization of light being transmitted. These materials are referred to as being optically active.

Atmospheric Scattering of Light

Light scattered from the atmosphere is partially polarized. Some animals appear to be able to detect this polarization and use it for navigation.

Atmospheric Scattering of Light

Scattered light in the atmosphere has an intensity that is inversely proportional to the fourth power of the wavelength. This means that shorter wavelengths dominate the scattered light, and accounts for the blue color of the sky.

This scattering, along with scattering off dust particles, also yields the red colors of sunset.

Review

Angular position of maxima in Young’s double slit experiment:

Separation between maxima at small angles:

Review

Light reflected from a boundary of a medium with a higher index of refraction undergoes a 180° phase change; if the index of refraction is lower, there is no phase change.

Minima of single-slit diffraction:

Maxima of a diffraction grating:

Review

Polarization is the preferential orientation of electric field vectors in electromagnetic waves. Light can be polarized by selective absorption, reflection, double refraction, and scattering.

Transmitted intensity of unpolarized light through two polarizers:

Reflected light is completely polarized at the angle: