Test 2 Flashcards
1
Q
Intensity for multiple slits:
What 2 phenomena’s do you need to combine to understand the intensity (I2)?
A
The phenomena of I2 in multi slit but also, Imax which is limited by diffraction envelope.
2
Q
what do you get when you combine the 2 phenomena’s for intensity with multi slits?
A
both intensity fromulas combined
3
Q
what is the envelope of intensity?
A
the function describing the diffraction minima
4
Q
What is light? EM radiation
A
electromagnetic radiation is a form of energy transferreed as waves of electric and magnetic fields
5
Q
EM radiation that humans see is what and what’s its wavelength?
A
visible light and the wavelength is between 400 and 700 nm
6
Q
what color is 700nm?
A
red
7
Q
what color is 400 nm?
A
purple
8
Q
How do EM waves transmit energy?
A
through a vacuum with a speed of 3E8 m/s (speed of light)
9
Q
Interference of light waves is done how?
A
light waves interfere by superposition
10
Q
what do we mean for electromagnetic waves?
A
we mean a specific component of electric or magnetic field
11
Q
what dimension do we work with in waves?
A
2 or 3 dimension
12
Q
what’s a wavefront? give an example.
A
just a line joining common points on the wave
Ex: all the peaks of the waves
13
Q
we are studying monochromatic light, what is it?
A
studying light that shine at only 1 frequency and 1 wavelength
14
Q
what are coherent sources?
A
sources of monochromatic waves that have a constant phase difference and we assume theyre always in phase
15
Q
what is polarization of wave sources?
A
the transverse wave disturbance lie along the same line
16
Q
is the interference of light waves the same as the interference for sound waves?
A
yes
17
Q
What is constructive interference?
A
when 2 waves of the same wavelength interact in a way where they are aligned and lead to a new, bigger wave
18
Q
what is an example of destructive interference?
A
where say we S1 and S2 and S1’s path to point c is exactly 2.5 wavelengths compared to S2. This means the wave crests arrive exactly one half cycle out of phase.
19
Q
to sum up: what is interference of light?
A
- waves interfere constructively if their paths lengths differ by an integral number of wavelengths
-waves interfer destructively if their path lengths differ by a half-integral number of wavelengths
20
Q
what do we do to observe two-source interference?
A
Young’s double-slit experiment
21
Q
describe Young’s double -slit experiment…
A
1-light is sent through a small slit
2-light encounters two other small slits S1 & S2
3-the waves emerging from S1 and S2 become coherent sources of monochromatic light
4-we see the 2 monochromatic coherent sources of light interfere with eachother on a screen
22
Q
when observing Young’s double-slit experiment, we see the light interfere with the screen and we see a light –> dark pattern, what do the light patterns mean?
A
bright bands= wave fronts arrive in phase interfering constructively
dark bands are the opposite
23
Q
how would you tell if the waves are interfering contrusctively or destructively?
A
their path difference
24
Q
how do you calculate path difference?
A
r2-r1 =d sin(theta)
25
which bands are bright?
constructive bands, m
26
which bands are dark?
destructive bands, m +1/2
27
what happens to the waves in Young's experiment?
the 2 light waves combine and create a a bright band (combined constructively)
28
can the waves combine constructively and destructively at the same time?
yes
29
give the equation for constructive interference:
dsin(theta) = m(wavelength)
30
give the equation for destructive interference?
d sin(theta) = (m + 1/2) (wavelength)
31
when can you use the small angle formula?
when it is less than 20 deg.
y = Rm(wavelngth)/ d
32
the closer together the slits are,...
the more the pattern spreads out
33
when the slits are far apart, the bands in the pattern are...?
closer together
34
what is intensity?
pattern of bright and dark fringes is often represented as an intensity graph
35
what is wave interference?
-two light sources shine onto a screen
-for intensity at a given point, we see...
constructive interference if path difference is integer number of wavelengths (in phase)
destructive interference if path difference is half-integer number of wavelengths (out of phase)
36
what does the phase difference look like if they arrive in phase?
0, 2pi, 4pi...
37
what does the phase difference look like if they arrive out of phase?
pi, 3pi, 5pi...
38
what is the phase difference symbol?
phi
39
what are phasors?
a vector where...
-the phasor's magnitude is the wave's amplitude
-the phasor's angle at any time is the wave's phase angle at that time
40
why do we use phasors?
to represent the intensity of one light source and another with a phase difference (acts as an angle).
41
what is the superposition of the 2 waves drawn as 2 different phasors?
Ip (intensity) is a new sinusoidal wave
42
when the 2 waves are half-cycle out of phase, what is phi? What would be the superposition of these two waves?
pi, 3pi, 5pi...
After turned into phasors, the 2 waves would give zero intensity because the vectors cancel out (dark fringes)
43
when the 2 waves are in phase, what is phi? What is the superposition of the 2 waves?
0, 2pi,4pi...
Superposition would be maximum intensity because the 2 vectors add up (bright fringes)
44
What's another way you can find the phase difference?
if you know the path difference, you can use that.
45
the equation for finding phase difference using P.D?
phase diff/ 2pi = path diff/ wavelength
46
when is it in between constructive and destrucutve interference?
when the phase difference is not a multiple of pi
47
what's the equation of the intensity of the light (relative to central bright) :
I2 = I1 cos^2(phi/2)
48
what happense when you shine a light through a single slit?
it causes a diffraction pattern
49
what's a diffraction pattern?
large central bright band, then alternating bright/dark bands
50
how do you find the location of the dark bands in a single slit experiment?
a sin(theta) = m(wavelength)
51
is the first dark band m =0 in signle slit?
no, not even in multiple slit
52
we have diffraction ***** and interference *****
diffraction minimas
interference maximas
53
do bright bands in interference patterns make it to I1?
no, they're modulated by diffraction patterns I max
54
d = Xa, xth interference is the ...?
missing maxima
55
what is another way of saying doffraction pattern?
fringe pattern
56
from geometric optics, we expect when we shine a light through a signle slit, to recieve 1 band, in reality we get...
a diffraction pattern.
57
Huygen's Principle is what?
in simple terms, it just describes how wavelets repeat themselves through times and just continue to cross over each other.
58
so how is diffraction made in the simplest term?
the wavelets interfere Huygen's wavelets) with one another creating diffraction patterns on screen
59
what is the path difference for diffraction of a single slit? Constructively?
p.d = a/2 sin(theta)
60
what would be the path difference for diffraction from a signle slit destructively? Dark fringes
a/2 sin(theta) = wavelength/2
asin(theta) = wavelength
61
take any pair of wavelets serrated by a/4, what will their p.d be?
a/4 sin(theta) = wavelength/2
a sin(theta) = 2(wavelength)
we can also divide them into sixth slits to find where they interfere destructively
a sin(theta) = 3(wavelength)
62
so we can confirm that the doffraction pattern for dark fringes is...
a sin(theta) = m(wavelength), m cannot =0 (0 is a bright fringe)
63
so since destructive diffraction is a sin(theta) = m(wavelength), what is it for the bright bands?
Constructive :
a sin(theta) - (m + 1/2) wavelength
64
Diffraction:
the wider the slit, the ....
narrower and sharper the central peak for intensity
65
does the small angle formula work for diffraction from a single slit?
yes, use : y = R m (wavelength)/ a
66
do wavelets arrive with it's own phase angle to reach a certain point?
yes, the phase angle between the wavelet from the top-most location of the slit with respect to the wavelet from the bottom location is called 𝜎.
67
when you calculate the intensity I1... what are the units?
rads because 𝜎 is in rads.
68
when dealing with intensity in single-slit patterns, if we want to know what it is for the first maxima, what formula will we use firstly?
asin(theta) =(m + 1/2) wavelength because we are dealing with bright
first maxima = m = 1
asin(theta) = (1.5)wavelength
secondly;
𝜎 = ...
69
whats the phase difference between for wavelet of single slit?
it's between the top and bottom wavelet
70
what do we know about 2 infinitsimally slits?
-they give an interference pattern with a constant intensity for each bright fringe
location of interferebce maximas is found by sin(theta) =m (wavelength)
71
what do we know about any true slit?
-has finite width
-introduces a diffraction pattern where each bright fringe has less and less intensity
location of diffraction minimas is governed by asin(theta) =m (wavelength)
72
now what happens when we have multiple slits but also considering that these slits have a width that causes diffraction?
resulting pattern is interfernece pattern but each interference maxima is modulated by diffraction pattern
73
what is the diffrcation curve representing?
envelope of intensity function
74
as we increase d, what happens to the interference maxima and the diffraction minimas?
the interference gets closer: sin(theta) = m(wavelength)/d
the diffraction stays in the same place (a is unchanged)
75
what happens as we increase a?
now, the diffraction minimas gets closer and the interference maximas are in the same place (d is unchanged)
76
when the interference pattern is modulated by the diffraction pattern, what information can we gather from it?
we can be told that the every i.e 4th interference maxima corresponds to a diffraction minima
this can help us find the missing maximas
77
how do we find the missing maximas?
make both equations equal to eachother
sin(theta)=sin(theta)
m(w.l)/a = m(w.l)/d
d/a = mint/mdif
78
for three slits, the resultant intensity to be zero is for the 3 sources to arrive at point ...?
120 deg out of phase from another
in diagram it looks like a triangle
could also be 240 deg out of phase drawn as an upside down triangle in ohasor diagram
79
with three slits, there's how many minimas possible?
2
80
as a rule there are always N-1 minimas between each ...
interference maxima (N is number of slits)
81
phasor diagram for 4 slits (3 slits till you reach the next maxima)
for dark fringe; square of vectors
for bright fringe; just add up the 4 vectors to a maximum
82
the equation for intensity in a Multi-Slit Interferance Pattern compares everything to ...
the central bright of that multi-slit pattern
83
if you were comparing it to the central bright of a SINGLE-SLIT interference pattern, what would you need to do?
multiply the intensity equation by N^2
84
what is diffraction grating?
thousands of slits will give a diffraction grating
-maximas become super narrow and basically look like lines
-theyre still an interference pattern dsin(theta)=mwavelength
85
the diffraction grating is basically...
an interference pattern with very sharp lines at an angle
86
in the diffraction grating process, longer wavelengths are...
at larger angles than shortr wavelengths
87
as we increase d what happens to the diffraction grating?
the maximas tighten
88
as we increase wavelength what happens to the diffraction grating?
the maximas soread out
89
what happens when we shine white light through a diffraction grating?
same thing as a prism, it breaks up the white light into many colours
90
whats the difference between reflection grating and reflected grating?
reflected light has a maximum intensity at angles where phase difference between light waves reflected from adjacent ridges is an integer of multiple of 2 pi
91
what must 2 light sources have for them to be seen as separate sources (resolved)?
angular separation (theta) of at least 1.22(wavelength/D)
92
what does not resolved mean?
you can't tell the two light sources apart
93
what is D in the formula for 1.22(wavelength/D) ?
diameter of the pupil or the device with circular aperture
94
why does circular aperture happen?
because the single source passing through D creates an airy disk with angular radius 1.22(wavelength/D)
95
what are these target like patterns in circular aperture?
diffraction patterns from circular apertures
96
what is the central bright maxima ?
airy disk
97
for theta 1 we have 1.22, what is theta 2 and theta 3?
theta 2= 2.34 and theta 3 is 3.24
98
Rayleigh's criterion is what?
we need to see the bump between them to see the 2 sources of light
99
what is the limit of resolution of the instrument?
it's the minimum separation of 2 objects that can be resolved by opticasl instrument using rayleigh's criterion = theta1 =1.22(wavelength/D)
100
what happens when we reflect a single light wave towards a thin film?
it reflects off the top and bottom of the thing film and you see 2 waves interfere
101
2 factors contribute to phase difference of waves ?
1- the phase shift that can happen upon reflection
2-the path difference of the 2 waves
102
shift from reflection is what?
wave will refelect half a cycle phase shift sometimes not
so 2 waves can be sent back to eye either in phase or out of phase
103
what will happen with the second factor of path difference?
wave transmited through the bottom surface will travel a tiny amount more (2t) than the wave that reflects from the top surface
104
for path diffrence what is the formula to find out whether they will arrive at your eye how they were sent?
integer number of p.d
2t =m (wavelength)
105
for them to arrive a half-cycle shifted from how they were sent?
half integer number is p.d
2t = (m +1/2) wavelength
106
how do you find the wavelength for any medium (with index of refraction n using the equation)
wavelength = initial wavelength/ n thin-film
107
what is a non-reflective coating?
a thin film meant to give destructive interference
108
to find the thinnest coating what do u use in the formula
2t = (m +1/2) wavelength?
m=0
so t =wavelengthn/4
109
what's the formula for finding how they were sent?
t = 1/4 x wavelength/ n(film)
110
why is it easier to performe interference experiments with lasers rather than ordinary light?
because lasers produce coherent light while ordinary light produces incoherent light.
the phase difference between waves emitted by ordinary light source change all the time so it's impossible to have constructive and destructive interference patterns
111
how would Young's experiemtn be affected if it was performed underwater?
Interference pattern would be compressed underwater but why?
-refraction index is the ration of speed of light through a vacuum to the speed of light in the medium
-n for water is 1.3
-speed is 1.3 times smaller in water than in a vacuum
-the speed of a wave is =wavelength x frequency
-since frequency doesn't change in medium, if v decreases, wavelength decreases too
-y=mL(wavelength)/d
now if m, L, d are the same,
y = wavelength so if wavelength decreases so does y making the int. pattern compressed underwater
