Astronomy Test 3: Part 1

The Nature of Light: Basic Properties

- Light travels in a straight line. - Most surfaces reflect light. • Amount of reflection depends on the medium. - Glass 4%, water 2%, aluminum 87%, silver 98% • When light reflects from a smooth surface, incident angle = reflected angle - When light travels from one transparent medium to another: • small fraction of light reflects . • refraction - e.g. When travelling from a media like air to a media like waster or glass light a ray refracts towards the normal, ⇒ angle of refraction is smaller than the angle of incidence.

Wave motion

-A wave is a disturbance propagating (moving) in a medium. Example: Waves on the surface of water

The Modern view of light

-According to the current understanding, light exhibits both particle and wave properties. (subject of the branch of modern physics Quantum Mechanics) -E = hf -Both particle theory and wave theory are correct. Each describes a different aspect of light. - When regarded as a wave it is described as an electromagnetic wave characterized by its frequency (or the wavelength) and the amplitude. - Also light can be considered as made of particles, called photons. • In that context light is a collection of photons, each having a specific energy depending on the frequency (color) of light. - energy of a photon: E = hf, h a constant (Planks constant), f frequency. • color ⇒ frequency ⇒ energy of the photon • Intensity ⇒ number of photons higher intensity ⇒ more photons

Thermal radiation (Black body radiation)

-All matter with a temperature greater than 0K emits EM radiation in a wide range of wavelengths. -Emitted radiation has a broad continuous spectrum: - its shape depends only on the temperature of the object, and is independent of its nature (composition), shape or size.

Formation of Mirages

-Cold air is denser than warm air and, therefore has a greater refractivity. -On a sunny day air near the ground is warmer and less refractive than the air higher up. -As light travels at a shallow angle along a boundary between air of different temperatures, the light rays bend towards the colder (upper) air and gets totally reflected.

Wave Theory of Light

-In addition to basic properties, wave theory of light was able to explain phenomena that did not have an explanation in the corpuscular theory. - like diffraction, interference, polarization. • But waves in what? - All known wave motion required a medium, (water waves, waves along a rope, sound waves in air...) - But light can travel in the empty space (vacuum), so the medium cannot be ordinary mater • 19th century physicists came up with various explanations, finally it was realized that light is a electromagnetic wave.

Wave motion

-It appears like a ripple is moving: - but particles in the medium only do a local cyclic movement. - only the disturbance (wave) is moving. Waves carry energy in the form of a disturbance, but not the matter in the media. -Variation causing the wave could be any property: - position of particles as in above examples - density, pressure - value of some field, like the magnetic or electric field as in the case of light, radio waves... - Epidemic, fashion

Radio waves

-Just like falling water droplet create water waves oscillating electric currents produce radio waves. -Heinrich Hertz -Since frequency can be anything, can there be EM waves with other frequencies? Maxwell believed there should be • He predicted the existence of low frequency EM waves 104- 106 Hz. • They (radio waves) were discovered by Heinrich Hertz in 1887. - Radio waves are produced by oscillating electric currents (charges) - which generates oscillating electric and magnetic fields and propagates away from the electrical conductor (antenna)

Secondary rainbow

-Light could reflect more than once inside a raindrop, producing higher order rainbows. -When light reflects twice inside a water droplet, a secondary rainbow is formed. • Due to extra reflection (only 2% of the light reflected) secondary rainbow is fainter. -Rainbows can form a complete circle, but the horizon only allows us to see half of the rainbow circle. From a mountain top or an airplane more of the rainbow can be seen -A rainbows can form whenever there are water droplets (mist) in air, and sunlight.

Newton: Nature of color

-Nature of color was first reveled by Newton through a series of experiments. He was the first to understand the color of the rainbow. They were published in 1704 in the book Opticks -(Shape of the rainbow was first explained by Rene Descartes in 1637, but he could not explain the color)

What is light?

-Newton proposed the corpuscular theory of light. That light is made up of little particles - called corpuscles. - A light source (lamp, light bulb) emits corpuscles. - They travel in straight lines in all direction from the source and bounce off (reflects) when they illuminate an object. - Corpuscular theory was able to explain many properties of light (reflection, refraction, color). In 1768 Christian Huygens proposed the wave theory of light. - According to the wave theory, light is a wave propagating from the light source. -According to Huygens light is a wave generated by the light source, like water ripples on a pond formed when a stone is dropped

Formation of Rainbows

-Rainbows are formed by refraction, reflection and the dispersion of sunlight in raindrops. -Angle between incident and refracted light is largest and brightest around 420 for red and 400 for blue. -⇒ inner ring of the rainbow is blue and outer ring is red

Electromagnetic Waves

-Thales (6thc BCE) noted that amber attracts feathers and other light materials when rubbed with fur - The first historical reference to static electricity. - (origin of the word electricity is from "ilektron" the Greek name for amber) • He also observed that lodestone attract iron, the magnetism. • Knowledge about electricity and magnetism was developed as two separate phenomena until the later half of the 19th century • In 1865, James Clerk Maxwell showed that electricity and magnetism are related, two aspects of the same entity, which he named electromagnetism. - He found that "electromagnetic waves" can exist and they travel at the same speed as light. - Thus he realized that light was nothing but electromagnetic waves traveling in space.

Types of Spectra

-Thermal dadiation -Mercury street lamp emission lines CFL lamp emission lines and bands -Spectrum of the Sun, continuous black body spectrum and absorption lines • To understand various features of the emission and absorption spectrums, we have to understand the light producing mechanism by atoms.

Temperature and pressure.

-When an atom bounce of the container wall, it imparts a force on the wall -In a gas atoms are always moving, at random velocities. • In a gas, particles (molecules, atoms) are always moving at random velocities. • Velocity of a gas particles increases with the temperature, • Temperature is a measure of how fast particles are moving. • The pressure of a gas in a container is the result of continuous collisions of gas molecules on the container wall. • Since the velocity of the gas particles goes up with the temperature pressure of a gas in a container increases when its temperature is increased

Atoms

-smallest unit of an element that maintains the properties of the element. -An atom consists of a nucleus surrounded by electrons. - Nucleus is made of positively charged protons and electrically neutral neutrons. • Nucleus accounts for nearly all of the mass of the atom. - An electron has a negative electric charge, it is approximately 2000 times lighter than the proton. • Electrons move rapidly around the nucleus and constitute almost the entire volume of the atom. • Size of an atom 0.1 - 0.5 nm, nucleus is 100,000 times smaller (1 nanometer =10-9meter) -An atom in the normal state has the same number of electrons and protons, so net electrical charge is zero.

red shift:

-wavelength gets longer when moving away from the Earth

blue shift:

-wavelength gets shorter when moving towards the Earth

Total internal reflection

1. When light goes from a high refractive medium to a less refractive medium (from glass to air for example), at larger incident angles light completely reflects without any light passing through. 2. total internal reflection. 3. For that to happen, the incident angle has to exceed a certain value. 4. critical angle (qc). for glass to air 41°, water to air 49°, diamond to air 28° (depends on the refractive index of the two media)

Few examples of total internal reflection (TIR)

Diamond refractive index = 2.4, TIR happens easily (qc=28°) , -Most light falling on the face of a properly cut diamond undergo several TIF inside diamond and leave it, causing it to sparkle -Prism binoculars use TIR in glass prisms as efficient reflectors

Rotation:

Different areas of the stellar surface move in different directions with respect the observer. - Towards and away at the edge near equator - red or blue shifted - Tangential in the central region - no Doppler shift. - No motion near poles. - no Doppler shift. - Spectral line will appear smeared out, center of the line darker than edges.

Terrestrial Applications of the Doppler effect

Doppler weather radar to map and measure the velocity of clouds RAdio Detection And Ranging Radar measure the distance to an object my measuring the time for the radio echo. The Doppler radar provide information about the object's speed in addition to distance.

Light as an Electromagnetic Wave

Electromagnetic waves : In an EM wave, strengths of eclectic and magnetic fields are changing in a cyclic manner, propagating like a wave. - Intensity of light depends on the amplitude of the wave. - Its frequency determines the color • red light frequency 4.6 x 1014 Hz, blue light frequency 6.7 x 1014 Hz • usings=𝜆𝑓(slide15)⇒ 𝜆=𝑠 𝑓 (s=speedoflight3x108m/s) wave length of red light: ~650 nm, wave length of blue light: ~450 nm (nm nanometer, 1 nm= 1x10-9m. thickness of paper ~60,000 nm)

Equivalence of Matter and Energy : 𝐸 = 𝑚𝑐2

• Long held view was that matter was conserved - Only change form one form to other in reactions, - cannot be created or destroyed. • In the early 20th century, Albert Einstein showed that matter and energy are interchangeable. - Matter can be converter to energy, and energy can be used to create matter. • Relationship between them are given by the formula 𝑬 = 𝒎𝒄𝟐 E: amount of energy produced when a mass m is converted to energy and vice versa . (c: speed of light) • 1 gram of mass converted to energy: - equal to the energy of burning 90 million gallons of gasoline. - same amount of matter converted to energy in the nuclear bomb dropped at Nagasaki. 1H1 +1H1 +1H1 +1H1 → 4He2 • In the Sun 600 million tons of hydrogen is converted into 596 million tons of helium every second. - 4 million tons of matter into energy (100 billion H bombs each second)

Wavelength (𝝀) :

the distance between two adjacent crests or troughs (or any two similar adjacent positions)

Amplitude (A) :

the magnitude of the wave at its peak.

Period (T):

the time it takes for one complete wave to pass a given point (or time to complete one cycle)

Emission spectrum

when a gas is excited it produces light with spectral lines at discrete wavelengths

Atmospheric absorption of EM radiation

• All types of electromagnetic radiation is produced by various kinds of celestial objects. • However, atmosphere is transparent only for two wavelength regions, in the optical region and in radio wave region. • To see with other types of EM radiation, instruments have to be placed above Earth's radiation absorbing atmosphere, in satellites, airplanes, or high altitude balloons.

Infra-red radiation scatters less

• Amount of light scatters depend on the relative size of the wave length of the light and size scattering particles. • If the wave length is larger than the size of the scattering particles it scatter less. • That is the reason blue light scatters more in the atmosphere than red light. Wave length of red light is larger in comparison to molecules and dust particles in the atmosphere. • Infra-red radiation has wavelengths even longer than the red light, so it won't scatter by even larger particles in the atmosphere, like tiny water droplets in fog/mist. • IR can be used to see through mist, fog or dust.

Inverse square law of light

• As distance to a light source increase, same amount of light is spread over a larger area, so the brightness (intensity of radiation) falls off. • Since surface area increases with the square of the distance brightness falls off as the inverse square of the distance (1/r2 ) ∝ 1/𝑟2

Thermal radiation

• As the temperature of the object increases: - it emits more radiation towards shorter wavelengths (higher frequencies). • Peak of the curve shifts to shorter wavelengths - Total emitted radiation (in all wavelengths) increases • This is in agreement with common experience: - When an object is heated, as the temperature rises its color chances from dull read to yellow to white

Doppler shift in Astronomy

• Due to the Doppler effect, wavelength of emission and absorption lines from celestial objects shifts: - blue shift - red shift • Measuring the Doppler shift of spectral lines can be used to estimate the relative velocity between the Earth and celestial objects. • A powerful tool in astronomy -Only the radial velocity contribute to the Doppler shift. (ie. component of velocity in the direction of line of sight).

If the source is moving towards the Observer:

• Each successive wave crest is emitted from a position closer to the observer than the previous wave. • Therefore, each wave takes slightly less time to reach the observer than the previous wave. • The distance between successive wave fronts is reduced in the direction of motion, • waves are "bunch together", shortening the wavelength (and increasing in the frequency).

The Nature of Matter

• Elements • There are 118 distinct elements, identified so far. 98 of them exist in the nature. Rest are man made using nuclear reactions. • Lightest elements hydrogen (H, 73%) and Helium (He, 25%) are the most abundant in the universe. - They were produced at the beginning of the universe (within first few minutes after the Big Bang). - The remaining natural occurring elements (2% by mass) were produced in stars.

Stefan-Boltzmann law

• Energy radiated by an object goes up with the temperature. Stefan- Boltzmann law gives the relation between them: - Amount of total radiation (energy) emitted by an object goes as the 4th power of the temperature. E ∝ 𝑇4 ⇒ 𝐸 = 𝜎 𝑇4 𝜎 a constant

Why an incandescent light bulb is so inefficient

• Filament temperature of an incandescent light bulb is about 3000k - This is in IR region, • most of the radiation form an incandescent bulb in the invisible IR region. • Only a small fraction (less than 5%) of the radiation is in the visible region. ⇒ incandescent light bulb is a very inefficient source of light.

Kirchhoff's Laws

• These facts were experimentally discovered by Gustav Kirchhoff and Robert Bunsen in 1860. • Their experimental findings were conceptually understood only in early 20th century, after the quantum theory of atoms and radiation was developed. • Essence of Kirchhoff's discoveries: -Thermal radiation -Emission spectrum -Absorption spectrum

Emission line spectrum

• This is the origin of emission spectral lines: - Each line in the spectrum corresponds to a photon emitted by the transition of an electron from a higher energy orbit to a lower energy orbit. -Since electron energy levels of are unique for each element, such transitions produce photons (light) with frequencies characteristic to the element, a spectral signature for that element -Energy of a photon E = hf ( h Plank constant, f frequency) ⇒ frequency f = difference in Energy levels/ h • Therefore by looking at the emission lines in an spectrum, it is possible to tell which elements generated that light, thus the composition of the source.

Electromagnetic Spectrum

• Visible light is only a small portion of a wider spectrum of waves known as Electromagnetic radiation, all travelling at the speed of light in empty space (vacuum) • Total spectrum spans from very low frequency radio waves to extremely high frequency gamma rays (g-rays). • Different frequency ranges have different names • Radio, microwave, infrared, visible, ultraviolet, x ray, g-ray ...

Absorption spectra

• When light passes through a cold cloud of gas the opposite happens. • Light is absorbed and electrons transit to higher energy levels. • This happens only with light with specific wavelengths, - only with photons whose energy is equal to the energy level difference (EX-E0). • So photons with energies matching the energy level differences of the gas atoms are absorbed by the gas. • In the spectrum those absorbed light appears as dark lines (missing light) at corresponding wavelengths, an absorption spectra.

Colors of stars

• When the temperature of a star is low (~3000K), it has more red light in the visible region so it looks redder. • At higher surface temperatures (10000K) a star has more blue light so looks bluer.

Light from Moving objects: Doppler effect

• When there is a relative motion between the source and the observer, it affects the received frequency of the wave. - First pointed out by the Austrian physicist Christian Doppler in 1842. • A well known example is the rising pitch of a train horn as a train approaches at a rail crossing and drop in pitch as it moves away. -When the source not moving, wave crests pass the observer at time intervals equal to the transmitted period of the wave. -If the source is moving, wave crests in the direction of motion are 'bunched together' (shorter wavelength) and in the opposite direction are spread out (longer wavelength) -when the source is not moving, all the wave crests are emitted and move out from the same point • Doppler shift can be observed for any type of wave - water wave, sound wave, light wave....

Doppler shift from binary stars:

• each star is alternatively moving toward and away. • spectral lines are periodically blue shifted and redshifted • spectral binary stars • Same technique can be used to identify planets orbiting stars (extra solar planets). -Rotation -Other factors: - Temperature, turbulences, (and pressure, magnetic field) all affect the spectral line shape

Thermal dadiation:

light from heated objects (ie. Incandescent lamp), continuous black body spectrum

refraction

light that passes through changes its direction

Elements

matter made of same type, can not be made by combining two other substances.

Brass

not an element, mixture of copper and zinc.

Frequency (f):

number of complete waves that pass a point in unit time: 𝒇 = 𝟏/t • usually measured in Hertz (Hz: cycles per second).

The Change in a Wavelength

radial speed between the source and the observer/speed of the wave x original wavelength

Thermal radiation

A hot solid object produces light with a continuous spectrum

Amount of bending (refraction) depends on many factors:

Angle of incidence: larger the angle of incidence more the deviation from initial direction. • The medium: some material refracts light more than other. - The refractive power, (ie. amount of bending) of the medium is given by the refractive index. Higher the number more it refracts light. - Water 1.3, ordinary glass 1.5, air 1.0003, diamond 2.4 • Color: - Blue light is refracted (bent) more than red light. - dispersion of light. -White light is a mixture of a continuous spectrum of colors, from red to magenta. -When a beam of white light passes through a glass prism, due to dispersion it is separated into different colors, forming a spectrum

Gas:

As the temperature increased further, atoms moves at speeds fast enough to get over inter atomic attractive forces and fly apart. They move in all directions, at speeds that increase with the temperature. It fills up its container.

Liquid:

At higher temperatures atoms vibrate faster. When the temperature is high enough atomic bonds break and atoms move around, still kept from flying apart by attractive forces between them. It take the shape of the container

Solid:

Atoms are held in a regular pattern by inter atomic forces. Atoms cannot move, but vibrate at an amplitude determined by the temperature.

emission nebula:

Gas excited by high energy (UV) photons from nearby hot stars

Thermal motion:

In a gas, particles are moving in random directions. Their velocities are depend on the gas temperature

Atomic Structure

In an atom electrons are held to the nucleus by electrostatic attraction: - Negatively charged electrons move around the positively charged nucleus. Electrons in an atom are arranged in different levels (or shells) around the nucleus. - It is like electrons are confined to a specific region, smeared out like a cloud, rather than in distinct orbits. - Each shell can hold only a specific number of electrons -Electrons in each level (or shell) have a specific energy. -Electrons in the shell closest to the nucleus have the lowest energy, upper levels have higher energies. • As the number of electrons in an atom increases (higher atomic number) they fill from lower levels to higher energy levels. (just like a glass fills from the bottom up) (natural tendency for any system is to have the lowest energy state)

Plasma:

Ionized gas. At very high temperatures (few thousands K) some electrons break free from atoms, making a mix of ionized (electrically charged) atoms and electrons. They are subjected to electrical and magnetic forces. It is the most common state of matter in the universe.

Proton

Mass (kg):1.673x10-27 Charge:+1

Neutron

Mass (kg):1.675x10-27 Charge:0

Electron

Mass (kg):9.1x10-31 Charge: -1

Spectral Binary Stars

Most binary stars cannot be separated visually, but can be identified from their periodical spectral line shifts

Isotopes

Number of neutrons in the nucleus could be different for the same element - There are nuclei with the same number of protons but different number of neutrons. - Chemical properties of an element depend only on the number of electrons and protons ⇒ it is possible to have atoms with same chemical properties, but different mass numbers.

dispersion of light

Refraction of different colored light by different amounts

ionized

When an atom lose any of its electrons

Speed (s) :

distance the wave travels in a unit time -Obviously, speed = wave length x frequency (length of one cycle) (how many of them pass a point in unit time) 𝒔 = 𝝀𝒇

Emission Spectra

When electrons move in between different energy levels they absorb or emit energy (light) • An atom in the normal state (ground state) electrons fill the lowest allowed energy levels. • When it is excited (by heating, electrical discharge, shining light on it) electrons can be moved to a higher energy level. • If the excitation energy is sufficiently large, electron could escape the atom. -ionized -An atom in an excited state is unstable, it always tries to return to the lowest energy ground state. When that happens, the atom releases excess energy as a photon (ie. light).

Absorption spectrum

When light passes through a gas it absorbs the same wave lengths of light it would emit when excited

Wien's displacement law

Wien's displacement law quantifies this behavior: - The wavelength at the peak of the radiation curve is inversely proportional to the temperature.

critical angle (qc)

The limiting angle this happens

Atomic Number

The number of protons (or electrons) in an atom determines its chemical properties

Water

formed by combining hydrogen and oxygen, not an element.

total internal reflection

This phenomenon that light is totally reflected at the interface between two media

Mass Number

Total number of protons and neutrons

Iron

an element, cannot be produced by combining two other materials