# Now that we have determined the solutions to the differential equation describing the oscillations of the electric and magnetic fields with respect to.

## Presentation on theme: "Now that we have determined the solutions to the differential equation describing the oscillations of the electric and magnetic fields with respect to."— Presentation transcript:

Now that we have determined the solutions to the differential equation describing the oscillations of the electric and magnetic fields with respect to time and position, we can determine a relationship between E and B. We can do this by substituting the solutions into one of the following equations. We will use the second equation since it is simpler. The ratio of the magnitude of the electric field to the magnitude of the magnetic field is a constant, specifically the speed of light!

The speed of light is a constant because the electric and magnetic fields support each other. If the speed of light was not constant energy would not be conserved!! Remember: Electromagnetic waves are a means of transmitting energy. The rate at which the energy is being transmitted is defined in terms of the Poynting Vector. S – Poynting Vector [W/m 2 ] For plane waves: We can also determine the intensity of the light from the magnitudes of the electric and magnetic fields. The factor of ½ is from the time average of the sinusoidally varying function that describes E and B in terms of position and time. If c increases in time spontaneously gain energy. If c decreases in time spontaneously lose energy.

Polarization Light is a combination of electric and magnetic fields. The orientation of the electric field vector defines the polarization of light. Polarization – Orientation of the electric field vector relative to the surface the light is incident on. The electric field vector is usually drawn to represent the direction of oscillation of the electric field. Light is polarized either parallel (p – polarized) to the surface, perpendicular (s – polarized) to the surface or a combination of the two. Normal light is unpolarized (or elliptically polarized). This means that light has no specific polarization. Polarized light has a specific direction of oscillation. When light is polarized along a single direction it is said to be linearly polarized. Unpolarized light Linearly polarized light Polarization can occur due to: Transmission through certain materials. Reflection off of certain surfaces.

A dichroic polarizer is the most common method for controlling polarization. Common polarizers Dichroic polarizers Dichroic polarizers can be designed to linearly polarize light that is transmitted through them. The intensity is reduced as well. If unpolarized light is incident on a vertical polarizer, what would be the polarization of the light upon leaving the polarizer? Vertically polarized light. If a second polarizer with horizontal polarization is placed after the vertical polarizer, and the vertically polarized light from the first polarizer is incident on the second polarizer, what would be the polarization of the light upon leaving the second polarizer? No light. The second polarizer only allows horizontally polarized light to pass through, therefore the vertically polarized light will not pass through the second polarizer.

Light can also be polarized due to reflection. Light that is reflected from the surface contains only p-polarized light (polarized parallel to the surface). The s-polarized light is transmitted through the surface (for example light reflected off of glass or water). How do polarized sunglasses work?

When a ray of light is incident on two polarizers with their polarization axes perpendicular, no light is transmitted. If a third polarizer is inserted between these two with its polarization axis at 45° to that of the other two, does any light get through to point P ? 1. yes 2. no

When a third polarizer is inserted at 45° between two orthogonal polarizers, some light is transmitted. If, instead of a single polarizer at 45°, we insert a large number N of polarizers, each time rotating the axis of polarization over an angle 90° / N, 1. no light 2. less light 3. the same amount of light 4. more light gets through. The smaller the angle between two successive polarizers, the larger the amount of transmitted light.

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