Light is classified as a transverse wave even though no "particles" move in a light wave. Only transverse waves can be polarized. Since light can be polarized, it is classified as a transverse wave.
Light is also classified as an electromagnetic wave since it can pass through a vacuum. Light consists of an electric field and a magnetic field oscillating through space perpendicular to one another. Here are two representations of light as an electromagnetic wave.
Characteristics of light as electromagnetic radiation:
Theories of light:
Maxwell's Equations Maxwell showed that light is a traveling configuation of electric and magnetic fields. He formulated differential equations that proved that electromagntic fields spread in the form of polarized waves and at the speed of light. The speed of light is related to purely electric and magnetic quantities.
Maxwell's four equations include a generalized form of Coulomb's law called Gauss' law for electricity (describes charge and the electric field), a similar law for the magnetism (describes magnetic field), Faraday's law (describes the electric field produced by a changing magnetic field), and Ampere-Maxwell law (describes a magnetic field produced by a changing electric field, by a current, or by both).
In our lab, we will be using a Joly photometer to measure the intensity of an unknown light bulb. The photometer is a device that measures the relative intensity of light. It is moved back and forth until both of its sides are equally illuminated.
How this is asked on the AP B exam: KNOW the inverse square law! Be able to convert power in Watts to intensity in W/ms. This is given by
I = P/(4 p r2)
Light terms:
color
Primary colors of transmitted light
Secondary colors
Complementary colors
An applet that allows you to mix colors and pigments. Color
The colors of a thin film result from the interference of light reflected from the front and the back surfaces of the thin film. When the film thickness equals ¼ l, that color of light will be constructively interfered with as it reflects from the two surfaces of the film. All others will be destructively interfered with.
Polarized light waves are either vertical or horizontal. They are produced by passing light through a polarizer.
Huygen's Principle Huygen's Principle predicts the future position of a wave when its earlier position is known. "Every point on a wave front can be considered as a source of tiny wavelets that spread out in the forward direction at the speed of the wave itself. The new wave front is the envelope of all the wavelets - that is, tangent to them."
Huygen's principle explains what happens when a wave hits an obstacle and the wave fronts are partially obstructed. It predicts that waves bend behind an obstacle, or diffract. Since diffraction only occurs for waves, not for particles, it verifies the wave nature of light.
Huygen's principle can also be applied to refraction. It predicts, for example, that the speed of light is less in water than in air. Foucault experimentally determined the speed of light in water in 1850, verifying the wave-theory prediction.
Angstrom: 1 A = 1 x 10-10 m
Spectrum types: The top one is a continuous spectrum; the middle is an emission spectrum; and the bottom is an absorption spectrum.
An excellent applet that shows the emission (bright line) spectra of multiple elements. This is a wonderful resource that students can use when working with gas discharge tubes in the laboratory.
Another good resource showing elemental spectra.
Scroll to the bottom of the page to view other spectra.
Diffraction is used experimentally to determine the wavelength of light:
In 1801, Thomas Young experimentally determined the wavelengths of visible light, obtaining experimental proof for the wave nature of light. In his experiment, light from a single source falls on two closely spaced slits. If light behaved as a particle, we would expect to see two spots on a screen. Instead, Young saw a series of bright lines which he explained as a wave-interference phenomenon.
When the light falls on the two slits, it diffracts, spreading out. The diffracted waves from each slit constructively and destructively interfere. If the waves from the two slits travel the same distance, they are in phase, and produce a bright spot in the center of the screen. Constructive interference also occurs when one wave travels an extra distance that is a whole number multiple of a wavelength of the wave, producing bright lines on the screen. Destructive interference occurs when one wave travels a distance of one-half wavelength (or 3/2, 5/2, etc.) more than the other, producing dark lines on the screen. One sees a bright central spot on the screen, with alternating dark and bright lines (or fringes) on either side.
Since the distance d between the slits is very small compared to the distance to the screen, you can assume that the light rays emerging from each slit are essentially parallel. The light rays make an angle of q with the horizontal. The extra distance that one light ray goes is equal to d sinq.
Constructive interference for a given wavelength of light l occurs when
Destructive interference for a given wavelength of light l occurs when
In double slit diffraction, the intensity of the bright lines (or fringes) is greatest for the central bright spot and decreases for the higher orders. Except for the central bright spot, the position of the fringe depends upon the wavelength of light. As Young found, the central bright spot apppears as the original, undiffracted light. The higher order fringes, contain a spectrum of the light colors comprising the original light. Their position depends upon their wavelength. Young proved that one color of light is distinguished from another color by wavelength.
The image above shows how intensity varies with position (on the screen) for a double slit diffraction pattern.
The image above shows two waves of light that each pass through a slit of width d and travel the same distance before they arrive at the screen. They constructively interfere because both go the same distance and arrive in-phase.
The image above shows two waves of light that each pass through a slit of width d and travel to a screen. The wave on the bottom travels a distance of 1/2l farther than the top wave. The waves destructively interfere because they arrive at the screen out-of-phase by 1/2 l.
The image shows two waves of light that each pass through a slit of width d and travel to a screen. The wave on the bottom travels a distance of l farther than the top wave. The waves constructively interfere because they arrive at the screen in-phase.
The location of constructive interference fringes can be predicted using:
A 2 source interference applet.
A ripple tank applet. Another ripple tank applet.
A very good Double Slit Diffraction applet
Another diffraction applet
Good applet that relates ripple tank to dirraction pattern on a screen.
Single Slit Diffraction Applet
Another single slit applet which lets you vary slit width and slit to screen distance and determine how that affects the diffraction pattern.
Very good applet that shows both single and double slit diffraction
Light passes through a small slit and falls on a screen so far away that the light rays emerging from the slit are considered to be parallel. Light rays that pass straight through are all in phase and produce a central bright spot of undiffracted light.
Consider rays at angle q such that the ray at traveling through the top of the slit travels exactly one wavelength longer than that emerging from the bottom of the slit. The light ray traveling through the center of the slit will travel 1/2 wavelength more than that of one emerging from the top of the slit. This ray will destructively interfere with that passing through the top of the slit. Each ray passing through the bottom half of the slit will cancel with a corresponding ray passing through the top half. The rays destructively interfere in pairs. Thus, no light reaches the screen.
This occurs at angles given by
Broad bands (areas of light) occur at angles given by
The image below shows a graph of intensity vs position for a single slit diffraction pattern. Notice the wide central band and the much less intense secondary bands.
Single slit diffraction applet
diffraction gratingconsists of multiples of single slits that each act as a single slit, producing a much brighter pattern. Gratings are produced by machining very fine parallel lines. If a grating consists of 10,000 lines per cm, the spacing between the lines (D) can be found by first converting cm to m (yielding lines per m) and then taking the reciprocal of this number.
At the boundary between two different media, light is partially reflected and partially transmitted. If the incident medium is less dense than the transmitted medium, the reflected ray is inverted (it changes phase by 1/2 wavelength). If the incident medium is more dense than the transmitted medium, the reflected ray's orientation is unchanged.
Thin film interference is used to control reflection &/or transmission of light or heat at optical surfaces.
Thin Film Interference Applet
To work thin film interference problems, you must realize that a formula is not enough. You must also determine if a phase change occurred at the boundary:
Applet showing how polarized light is produced
Maxwell's theory of light predicts that light can be polarized since it is a transverse wave. The direction of polarization is taken as the direction of the electric field vector. Polarized light is said to be plane-polarized, or the oscillations are in a plane. In unpolarized light, the electric field vectors vibrate at all angles.
A polarizer produces plane-polarized light by transmitting only the component of light parallel to the axis. An analyzer determines if the light is polarized and what is the plane of polarization.
Light can also be partially polarized by reflection. If light traveling in air is reflected from a medium with index of refraction of n, the incident beam is completely polarized if the incident beam's angle is given by tanq = n.
AP Multiple Choice Questions:
Newton's Rings When a curved glass surface is placed in contact with a flat glass surface, a series of concentric rings is seen when illuminated from above by monochromatic light. These are called Newton's Rings. They are due to the interference between rays reflected by thetop and bottom surfaces of the very thin air gap between the two peices of glass (just like a thin film). Because the width of the air gap increases from the central contact point out to the edges, the extra path length for the lower ray varies, giving rise to a series of bright and dark lines.
AP Free Response Questions: