Emergency Int Img Notes.pdf

1.1 Particle Theory of Light Classic Physics: Started with Isaac Newton and his contemporaries who developed a “ray” or “corpuscle” theory for light Light acts and travels as a particle in a straight line unless bent by lenses and prisms (and then continues straight) Pin Hole Camera provides empir...

1.1 Particle Theory of Light Classic Physics: Started with Isaac Newton and his contemporaries who developed a “ray” or “corpuscle” theory for light Light acts and travels as a particle in a straight line unless bent by lenses and prisms (and then continues straight) Pin Hole Camera provides empirical evidence of straight line paths Camera Obscura Earliest written observations (470 BC - 320 BC) Mozi (Chinese Philosopher), Alhazen (Arab scientist), Aristotle (Greek Philosopher) De Radio Astronomica et Geometrica –Gemma Frisius -1545 - Oldest known published drawing of a camera obscura DaVinci Notebook, 1502 - Oldest known published clear description of a camera obscura Particle Theory of Light Einstein proved that he could shoot exactly ONE photon and knock loose exactly ONE electron on a metal surface. This solidified the belief that light is made up of particles. The wave theory of light pictures a light source as behaving much like a speaker on a stereo, but instead of sound waves coming off in all directions, the light source produces waves of light energy Light waves are transverse waves E - Electric Field B - Magnetic Field K – Propagation vector Wavelength - Distance from one peak to the next K is the spatial wave number, or how many times a wave repeats over a physical distance y=Asin(2(pi)kx) k=1/wavelength y=Asin((2pi/w)x) Phase shift of sine curve y=(Asin(2(pi)kx +theta) sin((2pi/w)x+pi/2) = cos (2pi/w x) A wave can also vary with respect to time, y=Asin(2(pi)vt + theta) V = number of cycles completed in 1 time unit, analo The index of refraction ( n ) describes the relative slowing of light in a medium: n = c/v gous to spatial wave number Frequency is measured in hertz 1 HZ = 1 cycle per second The period (T) of the wave is the inverse of the frequency (𝜈) and is the temporal analog of spatial or angular wavelength (time to complete 1 cycle) T = 1/v Full equation of a wave: 𝑦=𝐴sin(2𝜋𝑘𝑥−2𝜋𝜈𝑡+𝜙) Wave speed of propagation Knowing the number of cycles per second and the wavelength, we can calculate the speed of propagation of the wave For EM radiation the constant speed of propagation in a vacuum is approximately 3x10^8 m/s 𝑠𝑝𝑒𝑒𝑑=𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦×𝑤𝑎𝑣𝑒𝑙𝑒𝑛𝑔𝑡ℎ Speed will be lower inside any medium and will vary with the wavelength (frequency) of the light as well as environmental variables The index of refraction (n) describes the relative slowing of light in amedium: n = c/v distance=velocity x time Snell’s law: (N1 x sin (theta1) = N2 x sin (theta2) Light bends towards normal force when fast to slow Ray: vector drawn perpendicular to wavefront Recall, we declared the velocity of EMR in matter was a function of wavelength The variation of the index of refraction with wavelength is known as dispersion Normal dispersion describes when shorter wavelengths slow more than longer wavelength The amount of energy in a wave is dependent on its amplitude as well as its frequency Radiant Power, or Radiant Flux, 𝚽, is simply the total energy that passes a defined space per unit time from a defined origin Units of [J/s], aka Watts [W] Coming or going in any direction GEOMETRY INDEPENDENT Solid Angle (2D): thetarad= arclength/radius thetaradcircle= 2pi (3D)= surface area/radius^2 Thetaradsphere: 4pi Radiometry: Radiant Intensity Energy exiting a source. A point on an object off which EM energy bounces may also be considered a source! Radiant Intensity, I Measure of radiant power from a point source in a 1sr cone Units of [W/sr] Irradiance: Incident EM energy Number of watts hitting a finite area, regardless of where they came from W/m^2 Inverse square Law The total radiant flux in a given solid angle from a point source is a constant As you move further from the point source, the area of incidence increases. E(d) is similar to 1/d^2 Radiance: Energy exiting a source of finite extended area. Radiance = L Measure of radiant power per area from an extended source in a 1sr cone W/m^2 sr Extended source = not a point source E=Nhv = Frequency dependence Radiator Oscillators emit EM energy into the radiator and absorb EM energy. E is the energy h is Plank’s constant = 6.625 x 10^−34 J/Hz 𝜈 is the oscillating frequency N is a number that can only take integer values (it is the number of photons) Visible EM Sources Sources are characterized by their spectral power distributions Energy per time per wavelength at all visible wavelengths Radiant flux per sampled wavelength 𝑆𝑃𝐷𝜆=lim(∆𝜆→0) ∆Φ/∆𝜆 [w/nm] An object that is heated to a high temperature can emit radiation A blackbody is an object that gives off radiation at all wavelengths, which means that it has a continuous spectrum  Plank derived the theoretical model for calculating the full power spectrum of a blackbody. Wien’s Displacement Law states that the peak wavelength of black body radiation is inversely proportional to its temperature. Stefan-Boltzmann Law states that the total power emitted per unit area by a black body is proportional to the fourth power of its temperature. Radiant Power to Luminous Power The human visual system is not equally sensitive to all the energies across the entire EM spectrum EM energy translates to perceived brightness by attenuation through the so-called Photopic Response Function (or ‘V-lambda’) And Radiometry becomes Photometry Lumen (lm)- Unit of visible luminous power Analogous to the Watt Luminous Intensity: Radiant Intensity becomes Luminous Intensity Luminous Intensity (Iv) Measure of Radiant Intensity attenuated by the V-lambda curve Units of [lm/sr], aka Candela [cd] 1 cd emits 1 lm of luminous power into 1 sr Irradiance becomes Illuminance Illuminance,Ev, is Irradiance attenuated by the V-lambda curve Measure of the number of lumens hitting a finite area, regardless of where it came from Units of [lm/m2], aka [lux] Radiance becomes Luminance Luminance,Lv Radiance attenuated by the V-lambda curve Units of [lm/m2sr], aka [cd/m2], aka [nits] Frequency cannot change! In the absence of permanent absorption, there is no energy lost across the interface or within the different bodies Proof of this behavior derives from the wave equation which explains oscillatory motion and Maxwell’s equations which explain the behavior of the electric and magnetic fields Slit Experiment: Demonstrates wave nature of light Diffraction Patterns Key to stable diffraction patterns is structured geometric objects Interference Constructive interference: two waves on same side create one big wave, then separate back to 2 small waves  Destructive Interference: Two waves on opposite sides create flat line, then become 2 small waves For sustained interference to occur, the light must be stable and coherent ○ Temporal: Same wavelength ○ Spatial: Matched wavefronts ○ Can be derived from laser sources Most light sources are incoherent, changing phase on the order of every 10-8 ○ Ex. No interference from overlapping 2 flashlights We observe interference from these sources only when EM waves interfere with themselves ○ Happens with thin film interference, diffraction gratings ○ Divergent waves focused through an optical aperture Diffraction Theories Fraunhofer - source is plane coherent and distance D to image is large compared with slit width Fresnel: Better explains behaviors when small D. Maximum constructive interference occurs when the extra path length of the lower ray, dsin 0, is an integer multiple of the wavelength Ymax = m𝜆D / d Maimum destructive interference can be found at half integers ○ Ymax = (m+.5)𝜆D / d Multiple slit interference: More slits at constant spacing (d) narrows the peaks and increases the magnitude Wave amplitudes are additive but the intensity is proportional to Symmetrical peaks of interference are attenuated by the single slit diffraction envelope Take the product of the interference and diffraction calculations Diffraction Grating Multiple slits in a small area Typical grating causes interference fringes to form in a pattern Polarization of Light Wave description of light provides the best description of a property called polarization Polarization controlling the direction of vibration of the electric fields ○ Linear polarization ○ Circular Polarization Light energy obeys the laws of conservation of energy What goes in must come out Reflectance, Absorbance, and Transmittance:  Some objects absorb more light than others, some reflect more than others, and some transmit more than others. These characteristics are properties of an object, R(𝜆) + A(𝜆) + T(𝜆) = 1 Scattering Light’s interaction with unordered geometries Light can also collide with something in the object and reflect in another direction Scattering can affect the amount of light transmitted or reflected Absorption Chromophore- Absorbs light. Goniophotometry Power of a surface: P=(n2-n1)/r n2=inde of material entered n1=inde of material exited R=radius of curvature of surface In Air: P=(n-1)/r Raytracing rules: Rule 1: Rays that approach the thin lens parallel to the optical ais eit through f’ Rule 2: Medial rays (pass through the center), leave the lens without deviating 1/f’ = 1/u + 1/v