Light and Waves book: Images

Extramission theory, in which eye rays interact with sun rays

Light particles

Intromission theory, in which sunlight reflects off an object and goes into a person’s eye.

$Refraction$

Three rays of light being refracted by a plastic block.

Diagram of an electromagnetic wave.

Emission spectra of hot objects, such as light bulb filaments.

Timeline of different theories of light. Although necessarily imprecise, dark grey regions represent the dominant scientific view and light grey regions represent alternative views.

Seismogram of the first 30 seconds of California’s 1989 Loma Prieta earthquake. Modified from Wikimedia.

A wave on a rope.

Wave peaks, troughs, wavelength, and amplitude.

Electromagnetic spectrum, showing bands and wavelengths.

Transverse and longitudinal waves

Transverse surface wave with vertical polarization.

Schematic of Fizeau’s equipment for measuring the speed of light.

Map of fiber optic cable from Aurora, Illinois to Carteret, New Jersey.

Cars on a road, for showing relationship among wavelength, frequency, and velocity.

Cars slowing down when they drive through a bumpy region.

Wave that slows down when it goes through a slow region.

Transverse shear surface wave in a plane.

Longitudinal surface wave.

Two people putting pulses into a rope that travel toward each other.

Superposition of pulses on a rope. The two pulses have the same polarity on the left side and opposite polarity on the right side. The top row shows the pulses before they meet, the middle row shows them meeting, and the bottom row shows them after they have passed.

Two sine waves with different wavelengths added together.

Constructive interference and destructive interference.

Waves with nearly the same wavelengths add to produce a beating pattern.

Reflection of pulses off boundaries that have two different boundary conditions. The one on the left produces an opposite polarity while the one on the right produces the same polarity.

Standing waves in a rope. The solid line shows the position of the rope at a particular moment and the other lines show rope positions at other times.

Water waves hitting a concrete seawall and reflecting off it, with an antinode at the seawall. This forms exceptionally rough water called clapotis. Note the smoother water in the background, past where the seawall ends.

The first three harmonics for waves in a cavity.

Thin-film interference from a thin layer of oil on water. A single oil drop on a wet road.

Thin-film interference from a thin layer of oil on water. Light rays, with waves showing constructive interference.

A diagram of Newton’s rings.

Michelson Interferometer. Light enters from the left, is split at the beam splitter, goes to the two mirrors, recombines at the beam splitter, and then goes left toward the source and forwards to the screen.

$Diffraction Big Hole$

Diffraction effects of large holes.

$Diffraction Small Hole$

Diffraction effects of small holes.

Huygens’s principle applied to plane waves.

Huygens’s principle applied to diffraction through a small hole.

Huygens’s principle applied to diffraction through a big hole.

Diagram of double slit experiment.

Diagram of double slit experiment. Light paths are shown in blue.

$Diffraction Grating$

Diagram of a diffraction grating.

$Diffraction Grating Photo$

beam of white light shining into a diffraction grating from the left and being redirected into multiple beams.

Diagram of single slit experiment.

Superposition for a phase shift.

Superposition for an overtone.

A book’s energy being converted between different forms, but always conserved.

A pulse created at the center of a taut membrane at t = 0 and expanding outward, decreasing in amplitude as it expands while conserving total energy.

Spectrum of a fluorescent light bulb. Modified from Wikimedia.

An audio equalizer showing a sound spectrum.

Spectrum from a guitar playing the E2 note.

Emission spectrum from hydrogen atoms.

Power spectrum of an earthquake. Data from Behrooz et al., 2014

Light intensity spectrum of a “soft white” incandescent light bulb.

Absorption spectra of β-carotene. The left axis shows absorption for a concentration of 10 μmol/L and a thickness of 1 cm. The right axis shows the extinction coefficient in units of M−1cm−1. Data from Prahl, 2017.

A father pushing his daughter on a swing. She gains energy through resonance.

Resonance for standing waves on a string.

Chemical structure of β-carotene, one of several similar carotene molecules.

Rotation of a water molecule, showing the three rotational axes.

The three vibrational modes of a water molecule (shown with exaggerated displacements).

(Top) The sun’s spectrum. Black lines arise from absorption of some light frequencies through resonance with specific atom or molecule normal modes. (Bottom) The emission spectrum of sodium atoms.

Doppler effect from moving observers. The source is stationary, at the center of the circles, and three people observe the sound.

Doppler effect from a moving source. The source is moving to the right and sending out sound waves, shown with black circles, with a constant frequency.

Doppler shift analogy with cars on a road. The red cyclist is riding in the same direction as the cars, so cars pass her at a slower rate than they would if she were stationary. The blue cyclist is riding against the cars, so cars pass him at a faster rate.

Simulated redshift. The sun’s spectrum, including the Fraunhofer absorption lines (section 4.3.6), is shown on top. The bottom shows the spectrum that one would see if the sun, or a similar star, were moving away from us at 2000 km/s, showing redshifted absorption lines.

Redshifts and blueshifts for a non-rotating star on the left and a rotating star on the right (the axis is vertical, with the left side approaching and the right side receding).

Sound waves from a supersonic source.

A pendulum at four different time points, where T is the pendulum’s period. Blue arrows show the forces acting on the weight, red arrows show the net forces, and green arrows show the weight’s momentum.

Waves on a thin string that has equally spaced beads along it.

Diagram of a sound wave, showing air density differences, which correspond to air pressure differences.

Hearing ranges of some animals. The human range is shaded.

Waveforms of some musical instruments, showing different timbre. Sound samples from Philharmonia.

Scientific pitch notation, showing the names of notes on a keyboard and in written music.

The first three normal modes of open and closed pipes. Red lines show standing pressure waves.

Normal modes of membranes. The fundamental is mode (0,1), at the lower left.

Speed of water waves in deep water as a function of wavelength. The top axis shows the wave frequency.

A trochoid curve being created with a Spirograph drawing set.

The top panel shows the forces on molecules with red arrows. The bottom panel shows the same forces with red arrows, and the molecule velocities in black arrows.

Wind blowing over water, where air turbulence near the surface creates an uneven water surface.

Wave growth by wind.

Water level over time at the the two ends of Lake Erie, during April, 2020. The gray line is for the west end of the lake (the Fermi power plant, near Detroit, Michigan) and the green line is for the east end (Buffalo, New York). Data from NOAA.

String telephone.

Projections in a shadow.

(Left) Ray diagram for a shadow on flat ground. (Right) Ray diagram for an orthographic projection.

Shadow of a ball on a wall, showing the umbra and penumbra.

Diagram of a solar eclipse, not to scale.

Diagram of a lunar eclipse, not to scale.

Pinhole Camera.

Ray diagram of a pinhole camera.

Multiple images of the Sun during a partial solar eclipse, created by gaps between leaves on a tree acting as many small pinholes.

Examples of shadow-based vision. Upper images from Wikimedia (Euglena, planarian, chambered nautilus, zebra ark clam). The bottom row shows diagrams of these eyes, with photoreceptors in orange, nerve fibers in blue, and shadows in gray.

A incident pulse on a thin rope being partially reflected from the point where the thin rope meets a thick rope. The knot has essentially no effect.

Rays reflected from a surface.

Ray diagram for a corner cube retroreflector.

Close-up of a bicycle reflector.

Reflection of a candle in a plane mirror.

Ray diagram for reflection from a plane mirror.

Another ray diagram for reflection from a flat mirror, now for one eye. The orange part of the mirror shows the part of the mirror where the image appears.

Parallel rays entering a parabolic mirror and converging at the focus. Flat mirrors approximating a parabola.

Parallel rays entering a parabolic mirror and converging at the focus.

Parallel rays reflect at a spherical mirror and converge at the focus, which is halfway between the mirror surface and mirror center.

The image of a candle with a concave mirror.

The image of a candle with a concave mirror shown with many rays.

Concave mirror ray diagram. Between mirror and focus.

Concave mirror ray diagram. At focus.

Concave mirror ray diagram. Between focus and center.

Concave mirror ray diagram. At center.

Concave mirror ray diagram. Beyond center.

The four principal rays for a concave spherical mirror.

A convex mirror on a road.

Ray diagram of a convex mirror.

A sailor in a submarine looking through a periscope at a seagull.

The number 5 and its mirror image.

atural and unnatural mirror images of the cysteine amino acid. Cysteine image from Wikipedia

Different possible paths for light in empty space, of which the straight line path is the one that a ray of light actually takes.

Different possible paths for light to reflect off a mirror, of which only the solid one obeys the law of reflection.

Time taken for light to reflect off different parts of the mirror.

$Refraction Waves Diagram$

Diagram of waves slowing down and speeding up, refracting at each transition.

$Refraction Roller Skating$

Roller skating from a hardwood floor onto a carpet has the same refraction bending effect.

Refraction of a light ray going into a slower medium. The reflected ray is shown with a dashed line.

Diagram of how mirages work.

Diagram of apparent depth, showing that objects appear to be less deep than they really are.

$Refract Air To Water$

Reflection and refraction for a light source in air.

Reflection and refraction for a light source in air at critical angle.

$Refract Water To Air$

Reflection and refraction for a light source in water.

Examples of total internal reflection, showing a glass of water, optical fibers, prisms inside a pair of binoculars, and a diamond.

Ray diagram showing how cat’s eye retroreflection works.

Total internal refraction fluorescence (TIRF) microscopy. Diagram of experiment.

Common lens shapes.

Ray diagram and coordinates for converging lens.

Ray diagrams and coordinates for diverging lens.

Ray diagram for a converging lens, showing many rays between object and image.

Ray diagram for a converging lens, showing all four principal rays.

Ray diagram for a converging lens for an object inside of the focus.

Ray diagram for a converging lens for an object at the focus.

Principal rays for a diverging lens.

Diagram of a camera taking a picture of some flowers.

Cameras and related devices on the back of an Apple iPhone 12 Pro Max smartphone. Values given in parentheses are equivalents for a 35 mm camera.

$Human Eye Refraction$

Diagram of a human eye. The ciliary muscles are relaxed, so rays from a distant object come to a focus at the retina.

Diagram of a human eye with myopia, in which rays from a distant object focus in front of the retina.

A typical eyeglasses prescription.

A ray diagram for a microscope. Fo and Fe are the objective and eyepiece lens focal points, respectively. Each dark or light band on the optical axis represents 1 cm.

A ray diagram for a telescope. Fo and Fe are the objective lens and eyepiece lens focal points, respectively.

A lens with chromatic aberration.

An achromatic lens that corrects for chromatic aberration.

Rays entering a raindrop in the top and leaving in the bottom.

A person’s view of a rainbow, along with white scattered light on the inside.

$Fermat Refraction Lifeguard$

Paths that a lifeguard can take to reach a swimmer, and times for the different paths, showing that path C, which obeys Snell’s law, is fastest.

Light rays going through a converging lens, all of which take exactly the same amount of time to go from object to image.

Considering a turtle's view.

$Aquarium Refraction Problem$

Aquarium refraction problem

$Water Wave Refraction$

Water wave refraction problem.

$Fermat Refraction$

Fermat refraction problem.

$Sunset Refraction$

Sunset refraction.

A diagram of a yellow light ray entering a human eye and being absorbed at the retina.

Spectral sensitivity of human eye photoreceptors. The black dashed line is for rods and colored lines are for cones. These graphs have been normalized so that each one has a peak value of 1. Data are from Stockman, 1993 and Wyszecki, 1982

Image for black-and-white afterimage.

Comparison of human and dog views of the world. Color appearance for different light wavelengths.

Comparison of human and dog views of the world. A person's view. From MaxPixel.

Comparison of human and dog views of the world. A dog’s view.

A modern color wheel.

Red, green, and blue (RGB) color mixing using lights.

Close-up of an Apple iPhone 5s display.

Cyan, magenta, yellow, and black (CMYK) color mixing using pigments.

Diagram for determining colors from subtractive color mixing.

Excitation of cone cells by light, where L is for long-wavelength or red, M is for medium wavelength or green, and S is for short-wavelength or blue. Single 530 nm light input. Data are from Stockman, 1993.

Excitation of cone cells by light, where L is for long-wavelength or red, M is for medium wavelength or green, and S is for short-wavelength or blue. Mixture of 530 nm and 630 nm light inputs. Data are from Stockman, 1993.

Response spectra for the fictitious “CIE standard observer” with cones labeled X, Y, and Z. Data are from Mathematica ChromaticityPlot.

Chromaticity diagram, or CIE xy color space. Data are from Mathematica ChromaticityPlot.

A person scuffing his feet across a rug. Red arrows show the electric field, the black ball is a little bit of positively charged dust, and the green arrow shows the force exerted on the dust by the electric field.

The Earth’s magnetic field, shown with blue arrows.

(Left) Near field radiation from an antenna, in black, where the electric field arises from charge displacement, and the magnetic field arises from steady charge motion. (Right) Far field radiation, which is only well well-established several wavelengths away, where the electric and magnetic fields arise from charge acceleration.

Electromagnetic wave, showing factors that cause it to propagate.

Electromagnetic spectrum.

Scattering efficiency from particles of different sizes for red light (650 nm) and blue light (450 nm), where curves represent Mie theory. The top row shows the colors that are scattered most strongly.

Geometric scattering examples.

Rayleigh scattering. Scattering of blue light by a nitrogen molecule, but red light is unaffected.

Rayleigh scattering. Cause of blue sky.

Vertically, horizontally, and diagonally polarized waves.

Vertically and horizontally polarized waves on ropes that encounter picket fences.

Two or three polarizers in a row, shown as diagrams in the top row and as what one sees in the bottom row. Red arrows show light polarization, and lines and white arrows show polarizer transmission axes.

Diagram of an LCD display.

Blue sky is polarized due to Rayleigh scattering.

Vertically and horizontally polarized waves adding to create diagonal polarization.

Circularly polarized light wave.

A crystal of calcite showing two images of the background.

Color temperature scale, along with the approximate effective temperatures of some objects.

Illustration of a “disappearing filament pyrometer”, in which the filament temperature is adjusted until its color matches the background color.

Black and silver cars during the day and at night.

Carbon dioxide concentrations (blue), global average temperature (red), and ice ages (gray) over the past 800,000 years. Human evolution dates are rough estimates, but included to give a sense of scale. Carbon dioxide data are from Luthi, 2008 and temperature data are from Jouzel, 2007.

Blackbody radiation spectrum for 5000 K. Shading represents the experimental result.

Illustration of a vertically polarized green photon as a wave packet that moves at the speed of light. The vertical axis shows the electric field, the axis going into the page shows the magnetic field, and the shaded region indicates either the photon size or the probability of where it might be found, depending on the interpretation.

Equipment for observing the photoelectric effect.

Compton scattering. An incident high-energy photon (purple) ejects an electron and is also scattered as a lower energy photon (blue).

A radiometer, which spins in sunlight. This diagram shows how the momentum of light would cause it to spin with the white side moving away from the light.

A radiometer, which spins in sunlight. This diagram shows how differential heating of air molecules causes it to spin with the black side moving away from the light.

Function of laser tweezers. The laser light is shown in red and the force on the bead is shown in blue.

Doppler cooling. (Left) The atom is stationary so all laser beams appear the same color, which does not match the absorption color, and photons are not absorbed. (Right) The atom is moving to the right so the laser beam from the right is Doppler shifted to higher frequency, causing these photons to be absorbed.

Simulated result of double slit experiment carried out with individual photons.

Photograph of the ocean surface. The coherence length, shown with red arrows, represents the distance over which the waves are reasonably regular, before fading into new wave patterns. Photo from Wikimedia.

A wave packet as the sum of many component waves, according to the super-position principle.

Electric fields of short light pulses, on the left, and the corresponding energy spectra for those pulses on the right.

(Top) A matter wave function, showing a wave packet that is propagating along the x-axis. (Bottom) The absolute square of the wave function, which is the probability of the particle being at any particular position along the x-axis.

The same matter wave at three points in time, showing that it spreads out. The time is measured in femtoseconds (10−15 s).

A classical roller coaster. Gray shading represents a potential energy surface.

A quantum roller coaster. Gray shading represents a potential energy surface.

Three particles hitting a barrier. Each row represents a different particle, where the top one has high energy, the middle one has medium energy, and the bottom one has low energy. Matter waves for each particle are shown in green at the start, blue as the particle hits the barrier, and red after hitting the barrier.

Nuclear fusion tunneling, in which a proton, shown with a blue wave packet, tunnels through an energy barrier to fuse with another proton.

Ammonia molecule potential energy landscape. Dashed lines show the energy of room temperature molecules, which undergo umbrella inversion by tunneling through the energy barrier.

Chemical structure of a β-carotene molecule. The red region represents the electron cavity, within which many electrons can travel reasonably freely.

Potential energy surface, energy levels, wave functions (left), and probability distributions (right) for matter waves in a cavity.

Energy levels for a carotene molecule, showing the quantum number on the left. These levels are filled with 22 electrons. A transition is shown in which an electron in n = 11 absorbs a photon and moves up to n = 12.

Hydrogen chloride molecule, showing the chemical bond as a spring.

Potential energy surface, energy levels, wave functions (left), and probability distributions (right) for the hydrogen atom in a HCl molecule.

Potential energy surface, energy levels, and the first few wave functions for an electron in a hydrogen atom. Blue wave functions are for the 1s and 2s orbitals, and the magenta wave function is for 2p orbitals.

Some hydrogen atom electron orbitals, where darker regions represent higher probability of finding the electron at that position. Red dots represent the nucleus. All images use the same scale, the z-axis goes up-down, and the x-axis goes left-right.

Hydrogen atom energy levels and transitions between them (not drawn to scale).

Periodic table of the elements, showing the atomic orbitals of the outermost electrons. Periodic table from Wikimedia

Potential energy surface, energy levels, and wave functions for an electron around two protons (i.e. the H2+ molecule). Red lines indicate the proton positions.

The left and right wave functions represent 1s atomic orbitals around the separate nuclei (shown in red). They combine to create 1σ and 1σ∗ molecular orbitals around both nuclei, which have lower and higher energies, respectively.

Bonding and anti-bonding molecular orbitals as electron clouds. Red dots represent the nuclei.

Molecular orbital diagram for a hydrogen molecule, H2. Each atom contributes one electron, shown on the sides, both of which move to the 1σ (bonding) molecular orbital, shown at the bottom.

Energy level diagram, showing that absorption occurs if the photon energy matches the energy level difference.

The sun’s spectrum, showing the background blackbody radiation and the absorption lines, along with which atom or molecule creates them.

Energy level diagram, showing that emission occurs from atomic or molecular relaxation from an excited state to a lower state.

Emission spectra of several elements.

Energy level diagram of fluorescence. Balls represent individual molecules.

Energy levels and their occupation in a laser medium.

Diagram of a laser.

A matter wave packet propagating to the right that has standard deviation σx.

Diagram of a particle’s position uncertainty increasing over time. In this “phase-space” graph, the x-axis shows position and the y-axis shows momentum.

Diagram of Schrodinger’s cat thought experiment.

Experiment to test the EPR paradox. The photon source emits pairs of unpolarized photons that are entangled. When Alice observes that a photon has horizontal polarization, its entangled partner will instantly collapse to have vertical polarization, measured by Bob, and vice versa.

Matter wave interference without environmental interactions, which produces interference fringes.

The same interference experiment but with environmental interactions, with blue dots representing air molecules that scatter the matter waves, which now produces the classical result of one spot behind each slit.

Diagrams of tides. Balls falling toward the moon only spread out if they have different distance from the moon.

Diagrams of tides. The Earth and its oceans spreading out.

Gravitational field of the Earth. Longer arrows represent stronger gravity.

Comparison of a HCl molecule (left) and a binary star (right). In the molecule, hydrogen is gray, chlorine is green, and the bond is shown as a thick line. Signs show electric charges in the molecule and mass values in the binary star.

(Left) Forces on balls between two stars. (Right) Gravitational distortion summarized as an ellipse.

A rotating binary star on the left creates a gravitational field that distorts a circle into an ellipse. These distortions propagate away from the binary star as a circularly polarized gravitational wave.

Polarizations for gravitational waves. One full wave period is shown, which is half of the binary star period.

Extrapolation effect in which the sun is attracted to the extrapolated position of the Earth, based on where the Earth was 8 minutes earlier. This figure is very exaggerated.

A person reading a book, who can’t tell if he is being pulled down by gravity, or pushed up by acceleration.

Light being bent by gravity. (Upper) Starlight being bent by the sun’s gravity. (Lower) Light from a distant blue galaxy being bent around a closer red galaxy.