EM Waves, Light & Telescopes

Electromagnetic Waves

Oscillating charges create oscillating magnetic fields, which in turn create oscillating electric fields 

The result are oscillating electric and magnetic fields that regenerate each other while traveling on space

Electromagnetic Waves

E&M waves need not material medium to travel, the can travel in vacuum

E&M waves have the standard properties of waves

Speed of light = 3x10^8 m/s

Waves 

 The time required for a full length to pass a given point (one full cycle)

Period:

Frequency:

Number of oscillations per unit time

\mathrm{Frequency} = \frac{1}{\mathrm{Period}}

1 Hertz = 1 oscillation per second

For example, for a period of 2 seconds per oscillation, the frequency is ½ oscillations per second or ½ Hertz

The speed at which waves travel through a medium is related to the frequency and wavelength

Wave Speed

\mathrm{Wave \ Speed} = \frac{\mathrm{Wave \ Length}}{\mathrm{Period}} = \mathrm{Frequency} \times \mathrm{Wave \ Length}

 Waves

Vibrations are the source of all waves

For example electrons in the antenna of an AM radio station at 960 kHz vibrate 960,000 times each second, producing 960 kHz radio waves

Electromagnetic Waves

E&M waves need not material medium to travel

E&M waves have the standard properties of waves

Speed of light is 3x10^8 m/s

Electromagnetic Spectrum

Wavelength (m)

Light :

 E&M waves in the visible range of the spectrum

Normal: Line perpendicular to interface

Checkpoint 1

What color of light has the highest frequency?

Checkpoint 2

What color of light has the shortest wavelength?

Violet

Violet

Refraction and Dispersion of Light

Wave Refraction

The bending of waves due to change of speed

Refraction of Light

Light rays refract (bend) when they pass from one medium to another at an oblique (not straigth) angle

Refraction is the result of waves changing speed as they cross from one medium to anoter

Direction of Refraction

Waves bend towards the normal when going from fast to slow

 and

away from the normal when going from slow to fast

Checkpoint 3

If you want to spear a fish from above the water, do you have to aim higher or lower?

Image

Actual

Lower

Dispersion happens because the refraction of light is frequency dependent

This is because higher frequency light travels slower inside the prism

Slowest

Fastest

Dispersion of Light

Vision and Color

The radiation curve of sunlight is a graph of brightness versus frequency. Sunlight is brightest in the yellow-green region.

Sunlight

The ultraviolet catastrophe was solved by Max Planck.  Assuming that EM radiation was emitted in discrete packets (quanta) Plank was able to explain black-body radiation

Light Quanta

h = \mathrm{Planck's \ Constant} = 4.14 \times 10^{-15} eV \cdot s
\mathrm{Energy \ Chunks} = \mathrm{Planck's \ Constant} \times \mathrm{Frequency}

Plank's found the emission of radiation is quantized, meaning that radiation energy can only be transferred in chunks of size:

E = h f = h \frac{c}{\lambda}
1 eV = 1.6 \times 10^{-19} Joules

The Photon (Light Particles)

In 1905 Einstein introduced the concept of the photon to explain the photoelectric effect 

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Light is emitted and absorbed in packets called photons. The photon energy is proportional to the frequency of light and given by E = hf

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So, is light made out of particles or waves?

The Wave-Particle Duality

In quantum physics (the physics of sub-atomic scales) not just light but matter and energy must be  explained as both, particles and waves

In Einstein's Words:

It seems as though we must use sometimes the one theory and sometimes the other, while at times we may use either. We are faced with a new kind of difficulty. We have two contradictory pictures of reality; separately neither of them fully explains the phenomena of light, but together they do.

Light Emission

Charged particle or Photon

Atoms emit light when their electrons change from higher energy levels to lower energy levels

A photon is emitted when an electron gets de-excited

 Atomic Energy Levels

Explanation of Quantized Energy Levels 

Electrons can only be at discrete energy levels (orbit radius), because the circumference of their orbit has to be an integer number of their wavelength in order to form standing waves, otherwise the experience destructive interference

In 1924 Louis de Broglie's suggested that electrons have a wavelength. This explained the quantized energy levels of atoms 

Atomic Energy Levels

Electrons can only be at discrete energy levels (orbit radius), so that the circumference of their orbit is an integer number of their  wavelength 

1

2

3

4

5

1

1

1

1

 Atomic Energy Levels

Different atoms have different radius (potential energy) and thus different energy levels for their electrons

Emission Spectrum

If you disperse the light emitted by specific elements, you would get a characteristic spectrum for each element

Each element has different emission spectrum, which can be thought as the signature of that element

Checkpoint 4

On the emission spectrum of Hydrogen there is visible line at 660 nm, what is the energy of the photons producing this line ?

E = h f = h \frac{c}{\lambda}
c = 3 \times 10^{8} \ m/s
E = 4.14 \times 10^{-15} \ eV \frac{3 \times 10^8 \ m/s}{6.6 \times 10^{-7} \ m} = 1.9 eV
h = 4.14 \times 10^{-15} eV \cdot s

660 nm

Emission Spectrum

Each element has different emission spectrum, which can be thought as the signature of that element

Mostly hydrogen (Pinkish Color)

Planetary nebula are metal rich (Many Colors)

Hourglass Nebula

Ring Nebula

Absorption Spectrum

If electrons in an atom get excited by light, they absorb photons at the same specific frequencies as they would emit when de-excited 

Reflection of Light

Law of Reflection

The angle of incidence equals the angle of reflection

This Is the result of Fermat's principle of least time

Diffuse vs. Specular Reflection

Diffuse

Specular

Incoming light scattered in all directions

Incoming light reflected in one direction

Law of reflection holds in both cases, diffuse reflection is the result of rough surfaces

Mirrors

Mirrors are the result of specular reflection

Tracing light rays from original, to mirror, to eye allows us to construct the image

Checkpoint 1

Which person in the front row sees the guy with the hat (person F) in the mirror?

Non-Flat Mirrors

Image in a curved mirror is distorted from original

Convex Mirrors

Image from convex mirror is smaller and closer than original

Convex Mirrors

Image from convex mirror is smaller than original

Concave Mirrors

Image from concave mirror is larger and farther than original if object close to mirror

Concave Mirrors

We use concave mirrors to build telescopes in order to collect light and focus it to the detector or eyepiece

Lenses

Wave Refraction

The bending of waves due to change of speed

Refraction of Light

Light rays refract (bend) when they pass from one medium to another at an oblique (not straigth) angle

Refraction is the result of waves changing speed as they cross from one medium to anoter

Dispersion happens because the refraction of light is frequency dependent

This is because higher frequencies travel slower inside the prism

Slowest

Fastest

Dispersion of Light

Lenses

Curved surface of a convex lens causes light rays to converge, magnifying images

Convex Lenses

Curved surface of a concave lens causes light rays to diverge, shrinking images

Concave Lenses

Lenses

Telescopes

Telescopes are Light Buckets

The main purpose of telescopes is to collect as much light as possible while maintaining as much detail as possible 

Both the light gathering power and resolution of a telescope increases with the diameter/area of the telescope

Refractors vs. Reflectors

There are two ways to collect light in a telescope. By refraction or by reflection

Refracting telescopes use a primary/objective lens to collect light by refraction

Reflecting telescopes use a primary/objective mirror to collect light by reflection

Refracting Telescopes

Refracting telescopes have many disadvantages:

  • The become too long for not that much light collecting area 
  • Large lenses are extremely expensive to fabricate
  • A large lens will sag in the center since it can only be supported on the edges
  • Dispersion causes images to have colored fringes

Refracting Telescopes Suffer from Chromatic Aberration

Slowest

Fastest

Refracting Telescopes Suffer from Chromatic Aberration

Reflecting Telescopes

Reflecting telescopes use a parabolic primary mirror to collect light. Light is focused in front of the mirror, how you observed it without blocking the incoming light?

Reflecting Telescopes

Reflecting telescopes use either detectors or secondary mirrors to gather or re-direct the focused light from the primary mirror

Reflecting Telescopes

Professional telescopes use a detector placed at the focal point of the primary mirror

Telescope Magnification

M = \frac{\mathrm{Telescope \ Focal \ Lenght}}{\mathrm{Eyepice \ Focal \ Lenght}}

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Checkpoint 2

The telescopes we used in class have a focal length of 1200 mm. What is the magnification when using a 25 mm eyepiece?

M = 1200 mm/ 25 mm = 48

M = \frac{\mathrm{Telescope \ Focal \ Lenght}}{\mathrm{Eyepice \ Focal \ Lenght}}

Telescope Resolution

A telescope’s ability to discern detail is referred to as its resolution or resolving power

The better the resolution the smaller angular separations a telescope can dicern

Telescopes and Diffraction

Diffraction is the bending of waves around corners and gap openings

  • The smaller the opening the larger the diffraction 

The resolving power of a telescope is limited by the wave nature of light through a phenomenon called diffraction

  • Long wavelengths diffract more than short wavelengths, e.g. red light diffracts more than blue light

Resolving power is proportional the to the telescope diameter and inversely proportional to wavelength

Checkpoint 2

What would improve the resolution of a telescope?

Increasing the diameter of the telescope and Observing shorter wavelengths of light/radiation 

Space and Non-optical Telescopes

Space and Non-optical Telescopes

Only visible and short wavelength radio waves (10 cm - 10 m) reach the ground

Radio Telescopes

Long-Scale Interferometry

The Event Horizon Telescope

The image of a black hole, imaged by the Event Horizon Telescope and published in April 2019.

The Milky Way Observed at Different Wavelenghts

Telescope Instruments

Cameras and Charged Coupled Devices (CCDs)

Spectrographs

The End

 Waves

Vibrations create waves. A sine curve is a pictorial representation of a wave

The Bohr model of the atom is explained by de Broglie's equation

Virtual vs. Real Images in Lenses

Real Image

Virtual Image

Virtual vs. Real Images in Mirrors

Real Image

Virtual Image