Physics 4510 Optics
Homework Assignment Problem Set #4
(Turn in before class by November 29th)
1. (10%) Assume we move one mirror of a Michelson interferometer through a
distance of 3.142 × 10 −4 m and we see 850 bright fringes pass by. What is the
illuminating wavelength?
2. (10%) Looking into the Michelson interferometer, we see a dark central disk
surrounded by concentric light and dark rings. One mirror is 2 cm farther from the
beam splitter than the other, and λ = 500 nm. What is the order of the central disk
and the 6th dark ring?
3. (15%) If we coat glass ( n = 1.5 ) with another material ( n = 2.0 ), what
thicknesses give maximum reflection? Minimum reflection? Assume that
λ = 500 nm.
4. (15%) A Michelson interferometer can be used to determine the index of
refraction of a gas. The gas is made to flow into an evacuated glass cell of length
l placed in one arm of the interferometer. The interference fringes are counted as
they move across the view aperture when the gas flows into the cell. Show that
the effective optical path difference of the light beam for the full cell versus the
evacuated cell is 2l (n − 1) , where n is the index of refraction of the gas, and
hence that a number N = 4l (n − 1) / λ fringes move across the field of view as the
cell is filled. How many fringes would be counted if the gas were air ( n = 1.0003 )
for a 10-cm cell using yellow sodium light λ = 590 nm?
5. (15%) In a two-slit Young interference, the aperture-to-screen distance is 2m and
the wavelength is 600 nm. If it is desired to have a fringe spacing of 1 mm, what
is the required slit separation? If a thin plate of glass (n=1.5) of thickness 0.05
mm is placed over one of the slits. What is the resulting lateral fringed
displacement at the screen?
6. (15%) A metal ring is dipped into a soapy solution ( n = 1.34 ) and held in a
vertical plane so that a wedge-shaped film formed under the influence of gravity.
At near-normal illumination with blue-green light ( λ = 488 nm) from an argon
laser, one can see 12 fringes per cm. Determine the wedge angle of the soap film.
7. (20%) Write a computer program to add 7 harmonic waves together graphically.
These waves have the same wavelength and amplitude but each differs in phase
from the next by 20 o . (b) Write a computer program to show graphically that for
what value of the phase difference the resultant wave would have zero amplitude
assuming equal phase difference between each wave and its neighbor.
ff
I
I
EECg*(oo rlru# +
-fL
phaee
I
So1nh,n
el,:(l*rae*
is
f l
5 = )ot{
^o
o'ne f,9o br;6!a
#,i"t
An/ tL,,
fu{.*
*1: f,So
)
-fu1^l ar*. nl;ffn u*'.*- r"",;l! 6*
yt
, t'{,
t =)n
114
Jd+/ \ o = Snon
J{?.f+}xro-v)
Jd
r
A
o
=
-
n^
=
-
8go
= +iqrryn
For
tlq
u*'Iu
5 = +A
Tlq
f ot = lqra
m = -{-4
X
orrlco,ts
fl
l,'sk
e
+
1
8o,,oo
-f" ,
;{o.1,
=
=
gs,ooo
o'-
tcoX/fl
4fu
es"^{en ri*q
(
Fn. fL
six*h ol"rL niy
Yn =. 8o, oeo -tS
= 7 7r11 9u
tL;(4
'lhas"
ol,*
*o
^tf*al
i,
,b = a J ( > n = r { )
A,
Io.
{(^
;^*ur$*
{"{
s-Qco"ldt
+L *o{o,
$ rr Fhu't4{
+o
,t,f{
Fh*
f'tsir
n .
{ns^ sh{L
l,
I* = 5 + n
+I
=
T.^
**"
oroli",n *{o
.xffe.t"o^
Ao
flro{ +T
havk- }vraxin,,t**\ ou {!ucf,u u, , +L
h*.ux *o
lo-s gs,.r-fr*ot'ni4
;^1*r4*r.e,4 L-E
5t =
+
or
=]\-n
*h'c*\
d = ( a m '- r ) +
4h.
d = ( > * * l \' &
,o\=1,2"
FA= or lp) ---
4t1t
= (am-rr )
, n*o,f,2
9eqe'n
4 (z:
= (>ry1+\)(6>.ln*)
T.
trwu,
i*onw1 ,x$o*t;nn
&,nin
,
$
5.t = ct-t'n.A/h,fy'
'
fiao, 1,L.._
d.uqbr^ch;ut;^{zn(*,r**x
= (zm+t)fi ld=o,frz
4rt t
= )m(bz.9n*)
*=t,z.".
*
IM
'*t I
oftca'
l^4+k a^ *fa
t
(,o-r!l
' P L ) " - , + U ' =J-1"
,(
\\
.'=
\\
(opl)-p^n, ln.t
{"tl
ettl
.t
_\
2
+t
oylicol
'oPD
I
I
po+
!,, o{,#-era,^ra
t t
= (opl)f,^rr (opL)^.n+6
?- Jn,Q.
a,{
=Jfull/{"
n^*h*r "f
ah.k #,\u )
+C,"+,"
, l+
AJ
$;,4o'
( ,'n./*
al,'Z br;6h1^^ol
Vrn-t)l
N:)T
= $(n-t)+
z\
A= l.ooo3, 1* =o.lna
N =
+(t"ooo3-t)to.t\
9?o X/o-9
h = (?of1n'lrn
= &o3
#1
a) F-.
+,.r
;,rf*,rlorc,na.
Yor"g
:p.
AX
-\
h
h =
\D
"
:
{dooxto-lJcVL =
ax
f . 2 rl1h4
fo.oo!)
b)
1l
lu
[Jn=,.,
o [=o .o h " ,^
+kr
OPD ,{
is
I.lo,^,,
S =
-
+*
&xtra
ir
a*
+k!
1uoo sfif s
aTi
hX
*,'fh
i^lw6sol
uff
+l*
,r*{sr;ol
{ t s
GPD
+L
*^1r*,'ol
s'= n{'o(
nrolw
*p
cane.eI
tl;g
y{.axo
VN i : !D = /n + \ A
x=
=
of$,f*t" *
- h d - P= - ( { . F } (o . € X r ; } J z t
h
lr. k aw\
(t. t r ro-t)
*..1.f\
l^'th
6
fr 'f &t*
f
{cm
- u' h n
3.gxto
tA" DPD +.
o\
{* o t'.-t,,.'/ie r*${utuA
+t4,..d ,l o./
r ur-iLeL ,
lEt
+Lo
o . oI
l r
AX
=
+ a K
^
i
E F D *= ).nd^
) n X'n *ind
Q.n 7^ c(
-$.
it^
o,d,)a.uen{+;,)T"s,
4h
oHo gh'"il r "t**! 1o
s*ll
$,
J
olt{fn cn"r ,(
a&
d^dr{2+h
yt,*l
a o P D = a n[ax) "1. = A
\
e
a
t
(
-
N
Zfi ax
e.IXle-9
J . t € x t ;,1- ( 8.Bxlo-s)
a( 1,3+)
"zrd, or
0.of3o
C:\Docs\MOptics\HW\HW4\prob7_1.m
August 1, 2005
% Problem #7 Part 1
clear all;
wt=0:.1:4*pi;
phase=20/180*pi;
E1=cos(wt+0*phase);
E2=cos(wt+1*phase);
E3=cos(wt+2*phase);
E4=cos(wt+3*phase);
E5=cos(wt+4*phase);
E6=cos(wt+5*phase);
E7=cos(wt+6*phase);
Etotal=E1+E2+E3+E4+E5+E6+E7;
plot(wt',[Etotal' E1' E2' E3' E4' E5' E6' E7']);
Page 1
10:24:49 PM
C:\Docs\MOptics\HW\HW4\prob7_2.m
August 1, 2005
% Problem #7 part 2
% phase = 360/7=51.43
clear all;
wt=0:.1:4*pi;
phase=51.43/180*pi;
E1=cos(wt+0*phase);
E2=cos(wt+1*phase);
E3=cos(wt+2*phase);
E4=cos(wt+3*phase);
E5=cos(wt+4*phase);
E6=cos(wt+5*phase);
E7=cos(wt+6*phase);
Etotal=E1+E2+E3+E4+E5+E6+E7;
plot(wt',[Etotal' E1' E2' E3' E4' E5' E6' E7']);
Page 1
10:28:13 PM
Part 1
6
4
2
0
-2
-4
-6
0
2
4
6
8
10
12
14
10
12
14
Part 2
1
0.8
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
0
2
4
6
8