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Optics - Coggle Diagram
Optics
Total Internal
Reflection
Investigation
Light ray refracts away from normal (Glass-Air)
Critical Angle - Light ray refrac. along boundary
Angle incr further = total internal reflection (TIR)
boundary essentially becomes a plane mirror
Can only occur above crit. angle into less dense
substance
Critical Angle
At crit. angle, i(c), the r angle = 90°, sin(r) = 1
n1sin(i'c) = n2
sin(i'c) = n2/n1
i'c = sin-1(n2/n1)
Diamond Sparkle
White light enters and disperses;
Diamond has n of 2.417 = greater disperse
than any other substance; i(c) = 24.4°
Thus light ray may be TIR'd multiple times
before leaving causing greater disperse
of colours
Optical Fibres
Used in medical endoscope to see inside body,
in comms to carry light signals; light ray is TIR'd
when it hits fibre boundary unless radius of bend
is too small; comm optic fibre allows light pulses
from one end (transmitter) to the other (receiver)
Highly transparent for min. absorption of light which
reduces amplitude of pulses progressively the
further they travel
More Fibre
Each fibre has core surround w/ layer of cladding,
has lo-er refract index, reduce light loss from core
(Light loss also reduce pulse amp)
- TIR takes place at cladded boundary, light pulses would
cross boundaries if fibres in contact otherwise = insecure
signal, reaching wrong destination
- Narrow core to prevent modal (i.e. multipath) dispersion
Occurs in wide core as light along axis < light constantly TIR'ing; Pulse becomes longer w/ wider core, can merge
Note
Pulse dispersion w/ white light instead of monochromatic
Material/Spectral dispersion due to speed of light in glass
of Opt. Fib. depends on λ, (violet speed < red speed)
causes white pulse to be longer
Medical Endoscope contains 2 fibre bundles, inserted into
body cavity, illuminated using light sent through one of the
fibre bundles, lens over end of other fibre bundle forms image
of cavity, light for image travels along other fibre bundle
Has to be coherent - fib. ends at each end in same rel. positions
Double Slit
Interference
Young's Double Slit Experiment
Christiaan Huygens - first to suggest Light
wave nature (17th cent.), rejected for Sir Isaac
Newton's corpuscular theory of light (tiny particles)
Newton had better reputation and wasn't challenged
until 1803 by Young's demonstrated interference of light
Observation
kinda like standing waves??
Illuminate 2 closely spaced parallel slits (double slits)
use suitable light source, slits are coherent sources of
waves = emit light waves with a constant phase difference,
same freq; Young's Fringes = alternating bright, dark fringes
seen on white screen where diffracted light overlaps
Fringes evenly spaced parallel to double slits
rap: do not interfere, your fringes better stay young
Note to self
If single slit is too wide each part prod's a fringe pattern
which is displaced slightly from pattern due to adjacent
parts of single slit - dark fringe become narrower, contrast
lost between bright/dark fringes.
Fire My Laser
Low power laser can be used, fringes
must be displayed on a screen
(can damage retina on entering eyes
Interference
Bright Fringe - one slit reinforces light from the other, in phase
Dark Fringe - one slit cancels light from other, anti-phase
Fringe Separation (w) = distance between adjacent bright fringes depends on slit spacing (s), distance from slit to screen (D), light (λ)
w = λD/s
Fringe Notes
Meas. across several fringes from centre of
a dark fringe to another (dark easier to locate
than bright); 2 loudspeakers w/ same signal
generator can be used to demo interference as
they are coherent, points of cancellation and
reinforcements can be detected by ear
Use Young's Slit Equation to estimate sound λ
(if it's small enough ^w^)
Moar >:3
Interference
Coherence
Emit the same frequency and constant phase difference,
Each crest/trough from single slit always passes through
one of the double slits a fixed time after the other slit
Similar to ripple tank demo - straight waves from beam
diffract through 2 gaps, waves reach nearest one first, but
the same wavefront reaches 2nd slit after fixed time =
Time interval between same wavefront is constant
No interfere pattern w/ 2 light bulbs - random emission,
points of cancel/reinforce constantly change randomly
Wavelength & Colour
White light w/ continuous spectrum - Red fringe separation (w) > Blue (w) due to formula~
Light Sources:
Vapour Lamps & Discharge Tubes - light w/ dom.
colours ("Na" lamps prod. yellow/orange - 590 nm)
effectively monochromatic
Filament/Sun Light - composed of colours
of the spectrum, continuous range, light from colour
filter is of particular narrower λ range than white light
Laser Light
Monochromatic - ~1 nm λ range
He-Ne Laser produces Red light, 635 nm, almost perfectly parallel & monochromatic; Convex lens can focus it to a very fine spot power conc. on small area
eye lens can do this, destroying your retina
Laser: Coherent Convenience
Lasers are a source of coherent light unlike other sources
Light emitted when e- moves down an energy level inside atom; e- emits a photon (packet of EM waves of constant
freq.) In a laser, each emit photon causes chain effect
stimulated photons are in phase w/ photon before them
Non-laser = atoms emit photons at random = random phase
White Light Fringes
Central fringe for different λ are in the same position on screen; in white light fringes, the central fringe is white as
every colour contributes at the centre of the pattern
Inner Fringes - tinged w/ blue on inner side, red on outer side
Outer Fringes - merge into indistinct background of white light,
becomes fainter w/ distance from centre, diff. colours reinforce, overlap
Refraction
of Light
Define it
Refrac. is change of direction as light passes at an angle
across boundary of 2 transparent substances; no Refrac.
if incidence ray is along normal; light ray bends towards
normal if it passes into denser substance, away if into
less dense substance
Refraction by Glass
Light ray box into rectangular glass at midpoint (P) of longer side - Incidecne angle between normal and light ray;
Refrac at P < Incidence at P; light leaves box at another point (Q); Refrac angle between PQ and normal
Snell's Law
Ratio of [sin(i) / sin(r)] is the same for each light ray
refractive index of substance, n = [sin(i) / sin(r)]
Partial reflection also occurs
Air-Glass v Glass-Air
i(1) = r(2); i(2) = r(1)
sin(i)1 / sin(r)1 = n; sin(i)2 / sin(r)2 = 1/n
Incidence ray entering block is parallel to
refracted ray leaving block
Triangular Prism Refraction
Path of monochromatic light ray through
triangular prism - ray refrac. towards normal
then refrac. away = curve, kinda
Diffraction
Observation
Diffraction - spreading of waves thru gap/edge
Important in optic design (camera, microscopes etc.)
Telescopes have wider gaps than eye pupil = less diffract.
More can be observed because of this
Greater Diffraction = gap is narrower/λ are larger
Each diffrac. λ-front has breaks either side of centre
- waves diffrac'd by adjacent sections on gap, anti-phase
in certain directions
Light Diffraction by a Single Slit
Can be demo'd by directing parallel beam at slit
Pattern - central fringe, further fringes w/ less intensity
Central fringe 2x outer fringe size, peak intensity decr.
w/ distance, outer fringes same width, much less intense
than central
More Single Slit Diffraction
Diff. sources of monochromatic light,
observations show greater λ = wider fringes
Adjustable slit shows narrow slit = wider fringes
Central fringe width (W) = λ/a * 2D
a = width of single slit, D = screen-slit distance
Single Slit diffraction...Young's Fringes
W/ double slit experiment, too wide, too far apart
slits = no interference pattern, interference only
when 2 slits overlap; each slit is narrow enough for
sufficient diffraction, close enough to overlap
Monochromatic...2 Apertures
λ wavelength, incident on 2 slits of aperture
width a at slit separation s (centre to centre)
Fringe Spacing of interference fringes:
w = λD/s
Width of Central Diffraction Fringe:
W = 2λD/a
Few interference fringes will be observed
in the central diffraction fringe if slit
separation (s) is small compared to width (a)
Moar 0w0
Refraction
Explaining Refraction
Caused by change of light speed in diff.
substances - amount of refraction depends on speed
of light in each substance; considering a wavefront
passing thru straight boundary we get:
sin (i) / sin (r) = c / c(s)
where c = light speed in vacuum, c(s) = l'speed in substance;
thus n(s) = c / c(s), smaller c(s) = greater refractive index
Note
Frequency of waves doesn't change (colour would change)
c = fλ -> c(s) = λ(s)f
n(s) = c / c(s) -> n(s) = λ / λ(s)
2 Transparent Substances
sin(i) / sin(r) = c1 / c2
sin(i)/c1 = sin(r)/c2 [times both sides by c]
sin(i) c/c1 = sin(r) c/c2
n1sin(i) = n2sin(r)
n = l'speed in a vacuum / l'speed in transparent substance
Light speed in atm. PSI = 99.97% of l'speed in vacuum
Thus refractive index is 1.0003 = ~1
White Light Spectrum
Use a prism to split white light from filament
into colours of spectrum - white light composed
of light w/ cont. range of λ from Red (650 nm) to
Violet (350 nm); shorter λ = greater refraction
Dispersive effect as l'speed depends on λ
Diffraction
Grating
Testing...s
Consists of plate w/ many close parallel slits - Parallel, monochromatic beam = light transmit in certain directions only - light passing thru each slit is diffracted, adjacent slits reinforce each other in certain directions only,
inc. incident light direction, cancel out all other directions
central beam = 0th order (same as incident); angle of
diffract between beams incr. w/ longer λ and narrower slits
Diffraction Grating Equation
Consider magnified view of part of diffract. grating
Each slit diffracts light waves, reinforces a λ-front
from a slit adjacent:
dsinθ = nλ
Number of slits per metre (N) = 1/d, d is grating space
For nth order and λ, smaller d value = greater diffract angle
Degree fraction expressed as decimal (.) or minutes (')
where 1° = 60' ; for max no. of orders produced, substitute
θ = 90° giving d = nλ and n = d/λ
Max no. of orders is the value of d/λ rounded to nearest
whole number
In Action
Cut parallel grooves close together on smooth glass plate,
groove transmits some incident light, reflects/scatters some;
grooves act as coherent emitters of like slits, but effective
slit width needs to be much smaller than grating spacing so
diffract waves spread widely, higher order beams would be
much less intense than lower order beams
Spectrometer
Study spectrum of light, measure light λ accurately
Designed to meas. angles to w/in 1 arc min. (1/60°)
Diffract angle can be measured very accurately;
w/ known λ, grating spacing can be meas. very accurately
Spectrum Analyser - electronic spectrometer linked to
CPU for visual display of variation of intensity w/ λ
Types of
Spectra
Continuous Spectra
Spectrum of light from filament lamp
is continuous (350 nm - 650 nm), most
intense part depends on light source temp.
Hotter source = shorter λ of brightest part
Line Emission Spectra
A glowing gas (vapour lamp/discharge tube) emits
light at specific λ so its spectrum consists of narrow
vertical lines of different colours - characteristics of
chemical element of produced light; more than one
element, elements in gas ID'd by line spectrum
Line Absorption Spectra
Continuous spectrum w/ narrow dark lines at
certain λ; Spectrum of filament lamp light
observed after passing it through a glowing gas:
thin dark vertical lines observed superimposed
on continuous spectrum, dark pattern due to elements
in glowing gas, elements absorb light of same λ they emit
Atoms that absorb, re-emit light but not necessarily in same
direction ^w^ done!