Optics, Waves, Lasers 2

Question 1

displacement of wave - angular

Answer 1

y(x,t)=Acos{wt}

Question 2

displacement of wave - linear

Answer 2

y(x,t)=Acos{2pift}

Question 3

displacement of wave if wave travelling with speed v

Answer 3

y(x,t)=Acos{w(t-x/v)}

can be other way around since cos theta = cos -theta

can also change depending on what variables given (w=2pif, f=1/T)

Question 4

wave number

Answer 4

k=2pi/lambda

Question 5

phase of wave

Answer 5

{kx+/-wt}

radians

Question 6

wave speed

Answer 6

v=dx/dt=w/k

Question 7

expressions for transverse velocity and acceleration

Answer 7

differentiating equation for y (partial diff)

Question 8

wave equation

Answer 8

consider d2y/dt2 / d2y/dx2 = v^2

rewrite as d2y/dx2=1/v^2 d2y/dt2

Question 9

combining hookes law with acceleration in SHM

Answer 9

ax=Fx/m=-kx/m

Question 10

energy in SHM

Answer 10

1/2mv^2+1/2kx^2=constant

Question 11

maximum displacement in SHM

Answer 11

energy is entirely potential energy (no kinetic)

can rearrange this formula for v

Question 12

total displacement

Answer 12

algebraic sum of displacements

*might need to use cos(a+/-b)=cosacosb-/+sinasinb

Question 13

principle of superposition

Answer 13

when two or more waves overlap, the resultant displacement at any point and at any instant is found by adding the instantaneous displacements that would be produced at the point by the individual waves if each were present alone

Question 14

standing wave

Answer 14

wave shape stays the same

zero points found when sin(kx)=0

Question 15

coherent

Answer 15

two monochromatic sources of same frequency and constant phase relationship

Question 16

constructive interference

Answer 16

if waves from two or more sources arrive in phases, then they reinforce each other

r2-r1=m lambda

Question 17

destructive interference

Answer 17

meet exactly out of phase
“cancel out”

resulting amplitude is difference of individual As, ie if same = 0

r2-r1=(m+1/2)lambda

Question 18

most reliable way to ensure light from two sources remains in phase

Answer 18

use of slits

Question 19

slit experiment

Answer 19

light through one slit then either of two

shone onto screen

bright spots=constructive

Question 20

approximate geometry used in slit experiment

Answer 20

treat rays as paraleel so r2-r1=dsintheta

can do this because distance R to screen&raquo_space; distance d between slits

Question 21

expression to find centres of bright bands on the screen

Answer 21

let ym be distance from centre to centre of mth bright band

theta m be corresponding angle for band

ym=Rtanthetam

since R»d, thetam very small so tantheta=sintheta

so sinthetam=ym/R

so dsintheta=dym/R=m lambda

hence ym=Rmlambda/d

Question 22

assumption in interference in thin films

Answer 22

assume light comes in almost vertically

Question 23

monochromatic light shining on air wedge

Answer 23

would expect pattern of C and D interference

in reality, pattern is reversed, dark regions at integer multiple and bright at 1/2 integer multiples. Phase shift is a result of Maxwell’s equations, EM nature of light

Question 24

na>nb

Answer 24

slow in first
Ei and Er same sign, no phase shift between incident and reflected

Question 25

na=nb

Answer 25

no refletion

Question 26

na<nb

Answer 26

slow in 2nd

Ei and Er opposite signs

phase shift or reflected relative to incident is pi radians

Question 27

let thickness of film bet t, if neither or both reflected waves have phase shift then

Answer 27

2t=mlambda CON

2t=(m+1/2)lambda DEST

Question 28

let thickness of film bet t, if one of the reflected waves have phase shift then

Answer 28

2t=mlambda DEST

2t=(m+1/2)lambda CON

Question 29

newtons rings

Answer 29

convex surface in contact with plane glass surface, creating a thin air film

circular interference pattern

Question 30

to avoid glare, need

Answer 30

destructive interference

Question 31

Huygen’s principle

Answer 31

from shape of wave at some instant, can work out shape at later time

new wave found by building a surface that is tangential to secondary wavelets

drawing diagram and zooming in shows low of refelction

Question 32

refractive index

Answer 32

ration of speed of light in vacuum to material

Question 33

diffraction

Answer 33

bending of light around obstacles

Question 34

spontaneous emission

Answer 34

direction and phase of photons emitted are random

shining light to absorb photon. Excited atoms return to ground energy and emit photon

Question 35

stimulated emission

Answer 35

each incident photon encounters a previously excited atom. Each excited atom emits a second photon with same frequency, direction and phases as incident photon.

two photons in phase - coherent

Question 36

number of atoms in state i

Answer 36

ni=Aexp{-Ei/kbT

therefore less atoms exist in higher energy states - negative exponenet

Question 37

population inversion

Answer 37

number of atoms in excited state > lower energy state

rate of energy radiation by stimulated emission can exceed rate of absorption, system will act as a net source of radiation

Question 38

steps to create population inversion

Answer 38

1. material pumped to excite atoms. (gas - electrodes used) High enough voltage, electric discharge occurs. Collision of atoms and electrons excite atoms
2. spontaneously emit, states depopulated. Atoms pile up in E2 as long lifetime. E2 more populated than E1
3. some E2 will transition to E1 and give off photons. Parallel mirrors send photons back and forth through gas, creating stimulated emission. Laser beam leaves as one mirror is partially trasnparent to desired wavelength

Question 39

holography

Answer 39

technique for recording and reproducing an image of an object through the use of interference effects

Question 40

how to make a hologram

Answer 40

illuminate object with monochromatic laser

place photographic film so that it is struck by scattering light and direct light

interference of the light forms interference pattern on film

to view: shine light through developed film creating virtual and real images