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PY 131 Chapter 26: Properties of Light

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.

R

PY 131 Chapter 26: Properties of Light

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.

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