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Sunday, 18 November 2018 03:32

Alexandre Costa

"EAAE Summerschools" Working Group

Escola Secundária de Diogo de Gouveia, (Portugal)

# Abstract

This Workgroup consist of an approach to spectrum theory of sunlight. The Sun is major source of almost all radiation bands, yet as our atmosphere has a high extinction at almost all non visible wavelenght's we shall only consider experiments on the visible infrared, and ultraviolet spectrum.

The workgroup will have a sequential theoretical presentation, mixed up with continuous experimental demonstration of all concepts presented. These demonstrations indicated in text, will consist of simple experiments that teachers can produce in class when introducing subjects like polarisation, extinction, continuous spectrum, line spectrum, sunlight spectrum and Fraunhofer lines, infrared using Herschel's experiment and ultraviolet interaction with chemicals.

Construction of simple spectroscope will also be done.

# Introduction

The Sun continuously radiates energy that spreads throughout space. The radiation is called electromagnetic because it propagates by the interplay of oscillating electrical and magnetic fields in space at a speed of 299793 kilometres per second.

A perfect linearly polarised electromagnetic radiation would have a profile like the one presented in Figure 1.

Sunlight has not preferential polarisation orientation, yet we can produce an oriented polarisation of sunlight using a Polaroid sheet. We can see that the light is polarised by placing another Polaroid sheet next to the first one and looking to the light passing through it. When the two Polaroid sheets have similar polarisation orientations (light will pass through them) or perpendicular polarisation orientation (light will be block and the sheets will be obscured)

(Demonstration 1).

As known, electromagnetic radiation can present different types of wavelengths or frequencies that are usually grouped in different types as shown in Figure 2.

Frequency, wavelength and light speed are related to each other by the expression

where ν is the frequency, c is the speed of light and λ is the wavelength.

Though the Sun is a major source of many wavelengths we will make the major part of our approach to sunlight spectrum using the visible, infrared and ultraviolet wavelengths, because except for radio frequencies those are that our atmosphere is transparent to (Figure 3).

Therefore they are the best ones for experimentation.

# Sun's Structure at a Glance

The Sun has five major structural parts that we can define:

• Core and radiation zone, that are the sites where the fusion reactions occur. The temperatures at that stellar interior are from 8 x 106 to 16 x 106 K, and the energy transport is all by radiation.
• Convection zone, where the energy is transported by convection, with temperatures below 500,000 K, under the photosphere and outer 0.3 sun's radius.
• Photosphere, which is the origin of continuous and absorption spectra, with temperatures ranging from 6400 K to 4200 K, and energy transport by radiation.
• Chromosphere, with energy transport by radiation and magnetic fields; temperature from 4200 K to 106 K.
• Corona, which is the source of solar wind, has temperatures from 1 to 2 x 106 K, and energy transport by radiation and magnetic fields.

It's common knowledge that the sun is a major nuclear reactor where huge amounts of energy are permanently being produced. The energy is transported to the surface in the form of photons. Photons are "light" particles responsible for electromagnetic radiation that have a quantified energy of value

where E is the energy of the photon, h is Planck's constant (h = 6,626 x 10-27 erg.s) and (ν is the frequency of the electromagnetic radiation associated with the photon.

Since the photons generated by the Sun are responsible for its spectrum, its spectrum will be a sum of al phenomena associated to the production of light since its nuclear generation until it leaves the Sun's atmosphere, as we shall now see.

# Opacity

In the Sun the energy associated to a photon takes typically 1 million years to reach the surface, since it is produced in the parts that are deeper than the photosphere and it will collide with mater that will absorb and afterwards emit it. The absorption's and emissions occur in a very big number since the generation of the photon until it reaches the photosphere.

When light reaches the photosphere, and consequently the atmosphere, it is radiated to the exterior without interactions for the major part of the wavelengths produced or with a continuous small interaction along all wavelengths and we call it this radiation the continuum.

The core and the inner parts of the Sun are opaque (optically thick) to all radiation wavelengths and its atmosphere is transparent (optically thin). A gas may be optically thin or optically thick according to the fact that it absorbs the photons crossing it. As an example, our atmosphere is normally optically thin to visible wavelengths. Yet, on a foggy day, you won't see far, so it is optically thick. But optically thin doesn't mean invisible. For instance one can use an overhead projector to prove that the flame of a burning candle is optically thin to visible light projecting the candle's shadow with an overhead projector on a wall.

(Demonstration 2)

The candle will appear, but not the flame. The flame is therefore optically thin to the wavelengths of the projector.

During the long period the photons stay inside the Sun they are thermalized, which means that the photons that are emitted will not have their initial wavelengths. Instead, they will have a distribution of intensities of emitted radiation that obeys a Planck curve, which is only dependent of temperature by Planck's law. For each frequency we will have

where h is Planck's constant, ν is the frequency, k is Boltzmann's constant 1.34 x 10-16 erg/K, c is the speed of light in vacuum, and T is the thermodynamic temperature.

We say it radiates like a blackbody. The distribution of blackbody intensity as a function of the wavelength is given in Figure 4.

All optically thick objects are blackbodies and they have a maximum wavelength (λmax) for emission of radiation associated to their temperature that can be determined by Wien's displacement law

where T is the thermodynamic temperature. Examples of optically thick astronomical objects are the stars (except for their atmosphere and corona), the planets, asteroids, etc.

Almost all things on Earth radiate like blackbodies. For instance, the common human being is a blackbody. It absorbs ultraviolet and visible light during daytime. Yet, as known, if one wishes to see the radiation emitted by him, one should seek the infrared region with the devices that military use. That is because all energy absorbed by the human being is thermalised and then emitted according to Planck's law close to a maximum infrared wavelength of 9.4 (m given by Wien's law (considering a temperature of 37ºC (310 K)).

Since the Sun's atmosphere is optically thin, the blackbody radiation will be determined by the temperature at photosphere (around 5800 K) so its blackbody radiation should have a maximum wavelength at 4900 Å, as shown in Figure 5. Also shown in Figure 5 are the ultraviolet and infrared absorptions due to the atmosphere as consequence of what has been presented with Figure 3.

Curiously the human eye has evolved to have a curve of visibility that is quite consistent with the visible curve of sunlight that gets to Earth's surface (Figure 6). Note that due to atmospheric extinction the light curve of sunlight reddens near sunset, and so does human eye visibility curve.

The concept of extinction can be demonstrated with an overhead projector leaking only a small beam, filling in small portions of a tall glass with diluted milk; the bigger the column of milk is, redder will be the light that gets to the wall, since blue light is preferentially scattered (Isn't the sky blue?)

(Demonstration 3).

# Absorption spectrum

When we have a hot atomic gas, it emits a line spectrum (2nd Kirschoff's law) associated to the emission of photons due to electronic transitions from a higher state to a lower state of energy (see Figure 7).

(Demonstration 4)

The relation between the energy levels and the frequency seen is given by

where EH is the higher level, EL is the lower level and h is Planck's constant. Viewing an incandescent lamp or an incandescent hot object with a spectroscope will allow us to see a continuous spectrum (1st Kirschoff's law).(Figure 7).

(Demonstration 5)

If the gas has those emission lines due to transitions between to electronic states, then obviously it can absorb the same energy doing the opposite transition. Then if the gas is put between an incandescent source and a spectroscope, the gas will absorb those same lines from the continuous spectrum of the incandescence source.

This is what happens in the sun's atmosphere. The gas of the atmosphere will absorb the frequencies associated to the spectral lines of the elements that it is formed of. Joseph Fraunhofer studied this phenomena in 1814, therefore the lines are called Fraunhofer lines. With a small portable spectroscope we can see many of the Fraunhofer lines.

Fraunhofer discovered about 700 lines (see Figure 8 for a high-resolution spectrum) but that makes a spectrum too complex that children cannot understand the interpretation of absorption spectrum as a consequence of the composition of the atmosphere. Low Resolution Spectrum as shown in Figure 9 however, will allow children to identify the major atomic composition by comparing the atomic emission spectrum with the absorption spectrum. Simple adaptations can be made to make the simulation not expensive (in black and white).

A low resolution spectrum can be seen using pocket spectrometers, that can easily be made with a tube, a diffraction grating and a paper with a line gap, putting the paper at one edge of the tube and the diffraction grating at the other

(Demonstration 6).

(Demonstration 7)

In 1800, Sir William Herschel discovered that the solar spectrum extended out beyond the portion that was visible to the human eye. He passed sunlight through a glass prism and formed spectrum. He used a blackened thermometers at several colours and compared the reading with that of a similar thermometer shaded from the spectrum close to the red end. He found a rise in temperature as he passed from the violet to the red end. The quite remarkable part occurred when he used a thermometer close to the red edge of the spectrum, but in the shadow, because that thermometer out of the shadow was even hotter then the ones on the spectrum. Herschel realised that there must be another type of light beyond the red, which we cannot see. This type of light became known as infrared.

# Ultraviolet Activity

(Demonstration 8)

Thanks to the ozone layer not too much ultraviolet radiation reaches Earth's surface. Yet, UV radiation is enough to produce suntan for instance.

We can show children the existence of ultraviolet radiation and how sun protectors can block it. We can show how the light of an UV lamp produces fluorescence on fluorescent materials.

Since money bills usually use fluorescent inks on it, we can demonstrate UV blocking effect by applying some sun protector on a transparency and showing it the under the UV lamp with and without interposing the transparency.