# Transmission of Electromagnetic Waves

Transmission refers to the process of an electromagnetic wave passing through a medium or across an interface between two media with different properties. When an electromagnetic wave encounters a boundary between two media, part of the wave will be reflected, and part will be transmitted into the second medium. The transmission of electromagnetic waves depends on several factors, such as the properties of the media, the angle of incidence, and the polarization of the wave.

The transmission coefficient (T) represents the fraction of the incident power that is transmitted at the boundary. It can be calculated using the relationship:

T = 1 – R

where R is the reflection coefficient, which represents the fraction of the incident power that is reflected at the boundary.

For normal incidence (θi = θr = 0), the transmission coefficient for the electric field (also called the amplitude transmission coefficient) can be calculated using the following formula:

T = 1 – |(n1 – n2) / (n1 + n2)|^2

where n1 and n2 are the refractive indices of the first and second media, respectively.

For non-normal incidence, the transmission coefficient depends on the polarization of the incident wave. As with reflection, the incident wave can be decomposed into two orthogonal polarizations: transverse electric (TE) and transverse magnetic (TM). The Fresnel equations for TE and TM polarized waves will provide different transmission coefficients for each polarization.

Transmission of electromagnetic waves has numerous practical applications, including:

1. Antennas: The transmission of radio waves through the air is essential for wireless communication systems, such as radio, television, and mobile networks. Antennas are specifically designed to transmit and receive these electromagnetic waves effectively.
2. Windows and filters: In optics, materials with specific transmission properties can be used to create windows or filters that selectively transmit certain wavelengths or polarizations of light. This can be useful in applications like photography, microscopy, and spectroscopy.
3. Fiber optics: As mentioned in the previous answer on refraction, the transmission of light signals through optical fibers is crucial for high-speed communication systems.
4. Greenhouse effect: The transmission of solar radiation through the Earth’s atmosphere and its subsequent absorption by greenhouse gases contributes to the warming of the planet. Understanding the transmission properties of different gases and their impact on climate is essential for addressing global warming.
5. Medical imaging: The transmission of electromagnetic waves through the human body is utilized in various medical imaging techniques, such as X-rays and magnetic resonance imaging (MRI). These methods help to diagnose and monitor various medical conditions noninvasively.

## Transmission Coefficient

The transmission coefficient (T) is a dimensionless quantity that represents the fraction of the incident power of an electromagnetic wave that is transmitted through a boundary or interface between two media with different properties, such as their refractive indices. It is complementary to the reflection coefficient (R), which represents the fraction of the incident power that is reflected at the boundary. The sum of the transmission and reflection coefficients is equal to 1:

T + R = 1

For normal incidence (θi = θr = 0), the transmission coefficient for the electric field (also called the amplitude transmission coefficient) can be calculated using the following formula:

T = 1 – |(n1 – n2) / (n1 + n2)|^2

where n1 and n2 are the refractive indices of the first and second media, respectively.

For non-normal incidence, the transmission coefficient depends on the polarization of the incident wave (TE or TM) and can be calculated using the Fresnel equations.

Here are five examples illustrating the transmission coefficients for different interfaces:

1. Air to glass: When light travels from air (n1 ≈ 1.0003) to crown glass (n2 ≈ 1.52) at normal incidence, the transmission coefficient is approximately:

T ≈ 1 – |(1.0003 – 1.52) / (1.0003 + 1.52)|^2 ≈ 0.961

This means that about 96.1% of the incident light power is transmitted through the air-glass interface.

1. Glass to air: When light travels from crown glass (n1 ≈ 1.52) to air (n2 ≈ 1.0003) at normal incidence, the transmission coefficient is approximately:

T ≈ 1 – |(1.52 – 1.0003) / (1.52 + 1.0003)|^2 ≈ 0.961

Here, again, about 96.1% of the incident light power is transmitted through the glass-air interface.

1. Air to water: When light travels from air (n1 ≈ 1.0003) to water (n2 ≈ 1.33) at normal incidence, the transmission coefficient is approximately:

T ≈ 1 – |(1.0003 – 1.33) / (1.0003 + 1.33)|^2 ≈ 0.977

About 97.7% of the incident light power is transmitted through the air-water interface.

1. Water to air: When light travels from water (n1 ≈ 1.33) to air (n2 ≈ 1.0003) at normal incidence, the transmission coefficient is approximately:

T ≈ 1 – |(1.33 – 1.0003) / (1.33 + 1.0003)|^2 ≈ 0.977

In this case, about 97.7% of the incident light power is transmitted through the water-air interface.

1. Air to diamond: When light travels from air (n1 ≈ 1.0003) to diamond (n2 ≈ 2.42) at normal incidence, the transmission coefficient is approximately:

T ≈ 1 – |(1.0003 – 2.42) / (1.0003 + 2.42)|^2 ≈ 0.833

About 83.3% of the incident light power is transmitted through the air-diamond interface.

The primary purpose of this project is to help the public to learn some exciting and important information about electricity and magnetism.