VL 11 Electromagnetic Radiation We Began This Course Studyin

Vl 11 Electromagnetic Radiation We Began This Course Studying

VL 11 - Electromagnetic Radiation We began this course studying electric charges, the electric field they generate, and the electric force they feel from external electric fields. We continued by examining the magnetic field generated by moving electric charges and the force external magnetic fields generate on other moving electric charges. We continued this thought process on how electric and magnetic fields can interact in our study of “light” or electromagnetic radiation. Refer to your text if you need a refresher.

1) Draw a representation of a light wave traveling to the right in the space below. Indicate the oscillating electric and magnetic fields. What is the direction of polarization of the EM wave you drew?

2) Now consider this wave and let it pass through a polarizing filter oriented with its polarization axis parallel to the polarization of the wave you have drawn above. How much of the wave passes through the filter? How does your answer change if the polarization axis of the filter and the wave are 45 degrees apart?

3) List some types of common electromagnetic radiation including microwaves, radio waves, x-rays, and the visible spectrum in order of wavelength from smallest to largest in the space below. Indicate the direction of increasing frequency with an arrow. How is the energy per photon related to the wavelength and frequency in the electromagnetic spectrum?

A black body or blackbody is an idealized physical body that absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence. The name "black body" is given because it absorbs all colors of light. A black body also emits black-body radiation. A black body in thermal equilibrium (that is, at a constant temperature) emits electromagnetic black-body radiation. The radiation is emitted according to Planck's law, meaning that it has a spectrum that is determined by the temperature alone (see figure at right), not by the body's shape or composition. Real materials emit energy at a fraction—called the emissivity—of black-body energy levels. By definition, a black body in thermal equilibrium has an emissivity ε = 1. In astronomy, the radiation from stars and planets is sometimes characterized in terms of an effective temperature, the temperature of a black body that would emit the same total flux of electromagnetic energy.

4) Please navigate to the Blackbody Radiation PHET here: spectrum/latest/blackbody-spectrum_en.html

a) At what wavelength does the earth emit? Would we say it glows?

b) At what wavelength does the lightbulb emit? Would we say it glows?

c) Though we hold our sun in unique regard it is in fact a very average star. What color would be describe it as? What is the “color” of the star Sirius A?

Paper For Above instruction

Electromagnetic radiation encompasses a broad spectrum of waves characterized by their wavelengths, frequencies, and photon energies. These waves are fundamental to understanding various natural phenomena and technological applications, ranging from communication systems to astronomical observations. This paper explores key concepts introduced in the course, including wave representation, polarization, electromagnetic spectrum classification, blackbody radiation, and their applications in real-world contexts.

Representation of a Traveling Light Wave and Polarization

A light wave propagates through space as an oscillating electric and magnetic field perpendicular to each other and the direction of propagation. In the illustration of a wave traveling to the right, the electric field oscillates vertically (say, along the y-axis), while the magnetic field oscillates horizontally (along the z-axis). The wave's polarization refers to the orientation of the electric field. For a linearly polarized wave, the electric field oscillates in a single plane. If the electric field oscillates vertically, then the wave's polarization is vertical. The magnetic field oscillates accordingly, perpendicular to the electric field and the propagation direction, which is along the x-axis.

Visualizing this, one can imagine sinusoidal waves for both the electric and magnetic fields, with the peaks and troughs aligned perpendicularly. The electric field's plane of oscillation determines the wave’s polarization. If a polarizing filter is aligned so that its polarization axis is parallel to this electric field, the wave passes through with maximum intensity. When the filter's axis is at 45°, the transmitted intensity is reduced according to Malus's Law, which states that the transmitted intensity is proportional to the cosine squared of the angle between the electric field and the filter axis. Specifically, if the wave's electric field is fully polarized in a certain direction, then at 45°, approximately 70.7% of the wave's amplitude passes through the filter.

Electromagnetic Spectrum: Wavelengths, Frequencies, and Photon Energy

The electromagnetic spectrum includes various types of radiation classified based on wavelength and frequency. From shortest to longest wavelength, the spectrum includes gamma rays, x-rays, ultraviolet, visible light, infrared, microwaves, and radio waves. The order is critical in understanding their properties and applications.

The spectrum in order of increasing wavelength is: gamma rays, x-rays, ultraviolet, visible light, infrared, microwaves, radio waves. Correspondingly, the frequency increases as the wavelength decreases, with gamma rays having the highest frequency, and radio waves the lowest. An arrow indicating the direction of increasing frequency would run from radio waves towards gamma rays.

Photon energy relates directly to the frequency via Planck's equation: E = hf, where E is the photon energy, h is Planck's constant, and f is the frequency. Because wavelength (λ) is inversely proportional to frequency (f = c/λ, where c is the speed of light), the energy per photon increases as the wavelength decreases. Thus, gamma-ray photons have enormous energies, whereas radio wave photons have very low energies.

Blackbody Radiation and Its Significance

A black body is an idealized object that absorbs all incident electromagnetic radiation, regardless of the wavelength or angle. It also emits electromagnetic radiation with a characteristic spectrum that depends solely on its temperature, as described by Planck's law. In practice, real objects are not perfect black bodies; they emit at a fraction of the blackbody spectrum, characterized by their emissivity (ε), which ranges from 0 to 1.

In thermal equilibrium, a black body emits continuous spectrum radiation with intensity distribution determined by its temperature, peaking at a wavelength inversely proportional to the temperature (Wien's Law). For instance, the Earth's infrared emission peaks at wavelengths corresponding to its average temperature (~288 K), predominantly in the mid-infrared range. This emission can be viewed as the Earth "glowing" in infrared, although at human-visible wavelengths, it appears dark.

Applications in Astronomy and Everyday Life

The concept of blackbody radiation plays a crucial role in astrophysics, where the observed spectra of stars are often approximated as blackbody spectra to infer stellar temperatures. For example, the Sun's spectrum peaks in visible light, giving it a white-yellow color, consistent with an effective temperature of about 5778 K. This peaks emits primarily in the yellow-green region of the visible spectrum, lending the Sun its characteristic appearance.

Objects like the Earth and lightbulbs emit infrared and visible radiation, respectively. The Earth emits primarily in infrared and can be considered to "glow" in that range, even though it is optically dark to human eyes. Lightbulbs, on the other hand, emit visible light and glow brightly, with their emission spectrum depending on their temperature and filament properties.

Color of Stars and Their Spectral Characteristics

The Sun's spectrum suggests a yellowish appearance, often classified as a G-type star, emitting most strongly in the yellow-green part of the visible spectrum. Sirius A, a brighter and hotter star, emits more energy in the blue and ultraviolet range, giving it a bluish-white appearance. The star's spectral classification and temperature determine its perceived color, which astronomers use to categorize stars and understand their physical properties.

Conclusion

Understanding electromagnetic radiation involves grasping wave properties, polarization, spectral classifications, and blackbody physics. These concepts are instrumental in many fields, from designing communication systems to interpreting astronomical data. The relationship between wavelength, frequency, and photon energy underpins our understanding of the spectrum's diverse phenomena, illuminating the nature of the universe and the objects within it.

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