Light

• Surrounding any electric charge is an electric field.

• Surrounding any moving charge is a magnetic field.

• Consider a charge which is oscillating in space.

  • the charge is continually changing its velocity i.e. it is accelerating.

• As the charge oscillates the electric and magnetic fields around it have to change with time.

• Maxwell’s addition to Ampere’s Law states that a changing electric field produces a magnetic field.

• Faraday’s Law states that a changing magnetic field produces an electric field. The disturbances in the fields move away from the charge.

  • Maxwell calculated this speed to be 300,000,000 m/s or 186,000 miles per hour. FYI the circumference of Earth is 24,901 miles. https://www.compadre.org/osp/EJSS/4126/154.htm

• Propagating disturbances in the electric and magnetic fields surrounding accelerating charges are called light.

• If we focus upon the disturbed parts of the fields then along a given ray away from the charge, the disturbances in the fields are transverse to the ray and look like

• the disturbances in the electric and magnetic fields are waves with a speed, frequency, wavelength and amplitudes.

• The speed of light is often given the symbol c.

• That light was a wave was already known well before Maxwell.

  • experiments had shown that two light sources could interfere

  • before Maxwell what wasn’t known was that it was a wave of

• From interference experiments the wavelength of visible light had been measured to be ~500 nm.

• Diffraction pattern of light from a laser as it passes through a small hole in a screen

• When part of a musical instrument vibrates (e.g. a string on a violin) it produces a note with the same frequency.

• When an electric charge vibrates, the light it produces also has the same frequency.

  • the slower the vibration the lower the frequency.

  • but unlike a sound wave, light does not need a medium: electric and magnetic fields can exist in a vacuum.

• There is no limit to the frequency at which a charge can vibrate. From the speed of light and the wavelength you can determine the frequency of visible light.

• the value is an eye-popping ~500,000,000,000,000 oscillations per second i.e. ~ 5 x 1014 Hz

• Maxwell found that the speed of light in a vacuum was the same for all frequencies.

The Electromagnetic Spectrum

• The range of all possible frequencies of light is called the electromagnetic spectrum.

• The EM spectrum is divided up into different ranges with each range given a name.

• The usual 7 categories of light are:

  • Radio waves

  • Microwaves

  • Infrared

  • Visible

  • Ultraviolet

  • X rays

  • Gamma rays

• The boundaries between the different categories are not sharp, they blend from one to the next.

The interaction of light and matter

• The oscillating electric and magnetic fields produced by accelerating charges propagate away from the charge.

• When those oscillating electric and magnetic fields encounter another free charge, they will cause it to start moving.

  • the charge gains kinetic energy from the light so the light transfers energy from one charge to another.

  • the energy content of the light depends upon the amplitude of the electric and magnetic fields

  • as the energy gets transferred to the charge, the amplitudes of the electric and magnetic fields must get smaller.

• The oscillating charge will emit light of its own in all directions

  • the charge doesn’t store the energy it absorbed.

• However most charges (electrons and protons/nuclei) are not free to move, they are bound inside atoms and molecules.

• An electron in an atom/molecule can only have particular amounts of energy (the same is true for protons in the nucleus).

• The electron can absorb energy from the light only if the frequency of the light is a particular value.

  • strong absorption of light occurs when the frequency is on resonance with the natural frequency of the electron

• Which frequencies are absorbed are unique to each element.

• When atoms are close to one another as in a liquid or solid, the absorption lines become wider.

• If the light passing by an atom/molecule cannot be absorbed, the atom/molecule still affects the light.

  • the atoms/molecules become polarized and/or magnetized and their polarization/magnetization fields alter the speed of light.

• The ratio of the speed of light in a vacuum to the speed of light in a material is called the index of refraction of that material.

  • index of refraction = speed of light in a vacuum / speed of light in material

• the index of refraction for water is 1.333

• the index of refraction of glass is ~1.5

• the index of refraction of diamond is 2.42

• These are at visible frequencies: some materials can have indicii of refraction closer to 10 for other types of light.

• Materials which do not absorb light are transparent.

• Transparency depends upon the frequency of the light.

• For example, glass is transparent for visible light but glass absorbs ultraviolet and infrared light

• Materials which absorb light are said to be opaque.

• The energy given to an electron that absorbed the light is then shared among the other atoms/molecules in the material and raises the average kinetic energy – i.e. the temperature rises.

EXAMPLE 1

What do radio waves infrared radiation, visible light, UV, X-rays and gamma rays have in common?

• they are all forms of light

Shadows

• Light travels in a straight line. A thin beam of light is called a ray.

• Consider a point source of light and an opaque object.

• Behind the object is a region called the umbra (shadow) where no light from the source can be found.

• The edge of the umbra is the ray that just grazes the edge of the object.

• If the light source has a finite size then in addition to the umbra, there is a region called the penumbra where some, but not all, the light can reach.

• The edge of the penumbra and umbra are again defined by the rays from the edge of the source which graze the object.

• For an extended source the umbra has a finite length if the source size is greater than the object size; if it is smaller then the umbra is infinite.

• The penumbra is always infinite and decreases in size relative to the umbra as the source becomes smaller or the object moves away.

• From the surface of Earth the Moon and Sun have, coincidentally, the same size in the sky

  • they are not actually the same size, the Sun is much bigger than the Moon but the Moon is a lot closer.

• If the Moon comes between the Earth and Sun then it’s umbra and penumbra can intersect the surface of the Earth.

  • Such an event is called a solar eclipse.

• Inside the umbra no part of the Sun can be seen: inside the penumbra only part of the Sun can be seen.

  • the Sun is said to be partially eclipsed inside the penumbra and totally eclipsed inside the umbra.

• The Sun is much bigger than the Moon so the umbra has a finite length.

• A solar eclipse where the umbra does not touch Earth’s surface is called an annular eclipse.

  • annular means ‘ring’, not that it happens every year

• If the Moon passes through the umbra or penumbra of Earth then we call this a lunar eclipse.

• due to light bent by Earth’s atmosphere the umbra from Earth on the Moon is not completely black, it is a very faint red.

The Eye

• The trajectory of light that enters the eye is changed by the shape of the cornea and lens.

• Rays of light are made to converge to a point that is on the retina of the eye.

• The process of making rays converge to a point is called focusing the light.

• By focusing light every point on a hypothetical spherical surface surrounding the eye is mapped to a point on the retina.

• The point where the rays cross is called the focal point.

• If the focal point is not exactly on the retina then the image is blurred.

• Objects in space are not all at the same distance from us so a single lens cannot focus the light from them all onto the retina at the same time.

• There is a range of distances called the depth of field where all the objects are in focus.

  • an object outside the depth of field will appear blurred.

• Blurry vision can also occur because the eye cannot correctly focus light onto the retina.

  • For example the shape of the eyeball or cornea is not spherical, or the lens cannot adjust to be the shape necessary to focus the light.

• Located on the retina are two different types of photoreceptor cell colloquially called rods and cones.

• There is a third type of photoreceptor cell called intrinsically photosensitive retinal ganglion cells but they are not related to vision.

• Rods are sensitive to brightness, cones are sensitive to color.

• Cones require bright light to function well.

• Cones come in three types called S-cones, M-cones and Lcones.

  • S, M, and L stand for short, medium and long

• S-cones are most sensitive to blue light which has a shorter wavelength

• M-cones are most sensitive to green light which has a medium wavelength

• L-cones are most sensitive to the longer wavelength red light.

• Rods are more sensitive to blue-green light than red

• What we call visible light is simply the light that is capable of triggering a response from the cones on our retina.

  • some birds and insects have cones on their retinas which respond to light that our cones do not.

• The range of wavelengths of light which form visible light is from ~400 nm to 700 nm, 4 x 1014 Hz to 7 x 1014 Hz. Light with the lowest frequency, and longest wavelength is red, and the highest frequency, the shortest wavelength is violet.

  • traditionally the six (seven) colors of the visible light spectrum (rainbow) are: red, orange, yellow, green, (cyan) blue, (indigo), and violet.