# PHYS 241

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### Huygen's construction or Huygen's principle

Each point on a primary wavefront serves as the source of spherical secondary wavelets that advance at the wavespeed for the propagating medium. The primary wavefront at some later time is the envelope of these wavelets.

### Fermat's principle

The path taken by light traveling from one point to another is such that the time of travel is a minimum. That is, light travels along the path of least time.

### Index of refraction

n = c/v where v = speed of light in the medium.

### Refraction

The change in direction of the transmitted ray.

### Angle of incidence

The angle between the incident ray and the normal.

### Plane of incidence

The plane containing the incident ray and the normal.

### Law of reflection

Angle of incidence equals angle of reflection.

### Snell's Law or Law of Refraction

n1sinѲ1 = n2sinѲ2

### Specular refraction

Reflection from a smooth surface.

### Diffuse refraction

Reflection from a rough surface.

### Total internal reflection

Phenomenon which occurs when the incident angle is greater than the critical angle, so no refracted ray exists.

sinѲc = n2/n1

### Dispersion

The dependence of the index of refraction on wavelength.

### Angle of minimum deviation

The reflected angle at which the intensity of light reflected is a maximum.

### Linearly polarized

When the electric field remains parallel to a line perpendicular to the direction of propagation.

### Transmission axis

Direction perpendicular to the chains of hydrocarbons on a Polaroid.

### Polarizer

The first of two polarizing elements placed in succession in a beam of unpolarized light.

### Analyzer

The second of two polarizing elements placed in succession in a beam of unpolarized light.

### Law of Malus

If the polarizer and the analyzer are perpendicular, no light gets through.

tanѲp = n2/n1

### Scattering

The phenomenon of absorption and reradiation.

### Birefringence

complicated phenomenon that occurs in calcite and other noncubic crystals and in some stressed plastics, such as cellophane. In such cases, light is separated into two rays: the ordinary ray and the extraordinary ray.

### Isotropic

the speed of light passing through the material is independent of the polarization of the light.

### Anisotropic

opposite of isotropic, biorefringent materials are because of their microscopic structure... speed of light changes in these materials due to the direction and propagation of the light.

### Optic axis

the direction in which both the extraordinary and ordinary rays propagate at the same speed.

### Quarter-wave plate

Plate whose thickness is such that a 90 degree phase difference exists between the waves of a particular wavelength when they emerge.

### Half-wave plate

Plate from which the rays emerge with a phase difference of 180 degrees.

### Circularly polarized

When the electric field vector rotates in a circle and has constant magnitude because the incident light was linearly polarized so that the electric field vector is at 45 degrees to the optic axis.

### Photon

A particle of light with Energy E = hf = (hc)/λ where h = 6.626 x 10-34 J-s = 4.136 x 10-15 eV-s

### Spontaneous emission

Random emission where the photons emitted from two different atoms are not correlated

### Rayleigh scattering

Scattering which occurs when the wavelength of incident light is large compared with the size of the atom.

### Inelastic scattering or Raman scattering

when an incident photon that has just the right amount of energy is absorbed and the atom undergoes a transition to a more energetic state.

### Stokes Raman scattering

when the energy of the scattered photon hf' is less than that of the incident photon

### Anti-Stokes Raman scattering

when the energy of the scattered photon is greater than that of the incident photon.

### Resonance absorption

when an atom absorbs a photon and making the transition to the more excited state

### Spontaneous emission

when an atom in an excited state spontaneously undergoes a transition to a less energetic state

### Fluorescence

when an atom is excited by ultraviolet light and emits visible light as it returns to its ground state by multiple transitions.

### Metastable state

an excited state with a relatively long lifetime - of the order of milliseconds or occasionally seconds or even minutes

### Phosphorescent materials

Materials that have very long-lived metastable states and emit light long after the original excitation

### Stimulated emission

when the atom is initially in an excited state of energy EH and the energy of the incident photon is EH-EL where EH and EL are the energies of higher and lower energy states. The oscillating electromagnetic field associated with the incident photon can stimulate the excited atom, which then emits a photon in the same direction as the incident photon and in phase with it.

### Compton scattering

when the energy of the incident photon is much greater than the ionization energy. In this type of scattering, a photon is absorbed and another is emitted.

### Image

The point at which the image forms in optical devices (P')

### Object

The point at which the original object is placed in an optical device (P)

### Virtual image

Image from which no light actually emanates (behind mirror, etc.)

### Depth inversion

The phenomenon that causes your right hand to look like your left hand in the mirror - a right-to-left reversal.

### Real image

An image from which rays actually diverge (in front of mirror, etc.)

### Paraxial rays

rays that are almost parallel to the axis and are near the axis

### Spherical aberration

blurriness caused by rays striking far from the axis and passing near the image point, but not through it.

### Focal length

r/2 for a spherical mirror

### Focal plane

the plane on which parallel rays incident on the mirror are focused

### Focal point

the intersection of the axis with the focal plane

1/s + 1/s' = 1/f

### Ray diagram

geometric construction of important rays and how they reflect off a mirror

### Principal rays

the three rays you need to draw to determine the final image location

### Parallel ray

drawn parallel to the axis, it reflects through the focal point.

### Focal ray

drawn through the focal point, it reflects parallel to the axis

drawn through the center of the curvature - it is reflected back on itself.

### Sign conventions for reflection

s is positive when the object is on the incident-light side of the mirror. s' is positive if the image is on the reflected-light side of the mirror. r, and thus f, is positive if the mirror is concave so the center of curvature is on the reflected-light side of the mirror.

m = -s'/s

(n2 - n1)/r

### Sign conventions for refraction

s is positive for objects on the incident-light side of the surface. s' is positive for images on the refracted-light side of the surface. r is positive if the center of curvature is on the refracted-light side.

### Magnification for a refracting boundary

m = -(n1s')/(n2¬s)

### Lens-maker's equation

1/f = (n/nair - 1)(1/r1 - 1/r2)

1/s + 1/s' = 1/f

### Converging or positive lens

a lens whose focal length is positive

### Diverging or negative lens

a lens whose focal length is negative (any that is thinner in the middle than at the top and bottom)

### First focal point

the focal point on the incident-light side of a converging lens, or on the refracted-light side of a diverging lens.

### Second focal point

the focal point on the refracted-light side of a converging lens, or on the incident-light side of a diverging lens.

### Focal plane

plane which intersects the axis of a lens at the focal point.

### Power of a lens

the reciprocal of the focal length: P = 1/f

### Principal rays for a thin lens

the rays you need to draw to determine the location of the final image formed from a thin lens.

### Parallel ray

drawn parallel to the axis; emerging ray is directed toward the second focal point of the lens

### Central ray

drawn through the center (vertex) of the lens. Ray is undeflected.

### Focal ray

drawn through the first focal point, emerges parallel to the axis.

### Near point

the closest point for which the lens of the eye can focus the image on the retina

### Simple magnifier

what a converging lens becomes when it is placed next to the eye with an object closer to the lens than its focal length.

### Magnifying power of a lens

M = xnear point¬/f

### Objective

the lens nearest the object in a microscope

### Eyepiece or ocular

the lens nearest the eye in a microscope

### Tube length

the distance between the second focal point of the objective and the first focal point of the eyepiece in a microscope.

### Magnifying power of a microscope

M = -(Lxnear point)/(fobjectiefeyepiece)

δ = (∆r/λ)*360°

### Phase difference due to reflection

If light traveling in one medium strikes the surface of a medium in which light travels more slowly, there is a 180° phase change in the reflected light.

### Coherence length

the length of a given "packet" of sinusoidal waves in nonideal light.

### Coherence time

the length of time it takes for a packet of light to pass a given point.

### Interference fringes

alternating bright and dark bands caused by viewing a thin film of varying thickness with monochromatic light.

### Newton's rings

circular interference fringes resulting from viewing light reflected from an air film between a spherical glass surface and a plane of glass in contact.

### Order number

m = 0, 1, 2... for two-slit interference maxima. m = 1, 2, 3... for two-slit interference minima.

dsinѲm = mλ

### Two-slit interference minima

dsinѲm = (m - ½)λ

### Lloyd's mirror

a method of producing a two-slit interference pattern.

### Central diffraction medium

in single-slit diffraction, the area where most of the light intensity is concentrated.

### Points of zero intensity for a single-slit diffraction pattern

asinѲm = mλ, m = 1, 2, 3,...

### Phasor

a vector which rotates in the xy-plane with angular frequency ω

### Intensity for a single-slit diffraction pattern

I = I0*[{sin(φ/2)/ (φ/2)}^2]

### Interference-diffraction intensity for two slits

I = 4I0[{sin(φ/2)/ (φ/2)}^2][{cos(δ/2)}^2]

### Fraunhofer diffraction pattern

diffraction pattern that is observed at a point for which the rays from an aperture or an obstacle are nearly parallel

### Fresnel diffraction pattern

Diffraction pattern observed near an aperture or obstacle.

### Rayleigh's criterion for resolution

when the critical angle of separation, αc = 1.22λ/D, separates two sources as seen through a circular aperture, the two sources will be seen as one source.

### Diffraction grating

tool used for measuring the wavelength of light which consists of a large number of equally spaced lines or slits on a flat surface.

### Spectral line

in a diffraction grating, each wavelength emitted by the source produces a separate image of the collimating slit

### First-order spectrum

the spectral line corresponding to m = 1.

### Second-order spectrum

the spectral line corresponding to m = 2.

Example: