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 410142.3 −× 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 500=λ nm. What is the order of the central disk and the 6th dark ring?

3. (15%) If we coat glass ( 5.1=n ) with another material ( 0.2=n ), what

thicknesses give maximum reflection? Minimum reflection? Assume that 500=λ 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 )1(2 −nl , where n is the index of refraction of the gas, and hence that a number λ/)1(4 −= nlN fringes move across the field of view as the cell is filled. How many fringes would be counted if the gas were air ( 0003.1=n ) for a 10-cm cell using yellow sodium light 590=λ 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 ( 34.1=n ) 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 ( 488=λ 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 o20 . (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.

ffII

EECg *(oo rlru # + So1nh,n-fL phaee el,:(l*rae* is

I f l

5 = ) o t {̂o

An/ tL,, o'ne f,9o br;6!a #,i"t ) *1 : f,So

fu{.* , t'{, -fu1^l yt ar*. nl;ffn u*'.*- r"",;l! 6*

t = ) n 1 1 4

Jd+ = Snon/ \ o

r J d J { ? . f + } x r o - v )A o = - = - 1

n^ 8go

= + i q r r y n f l

For tlq u*'Iu l,'sk

5 = + f ot = lqrae A

+ m = -{-4 = ; {o.1, = gs,oooX tcoX/fl

o'-

Tlq orrlco, ts 8o, ,oo -f" , 4fu es"^{en ri*q(

Fn. fL six*h ol"rL niyYn =. 8o, oeo -tS = 7 7r 11 9u

Io. {(^

lhas" tL;(4 ol,* *o ^tf*al i,'

, = a J ( > n = r { )b A ,

{"{ ;^*ur$* f'tsir

s-Qco"ldt n .

$ rr Fhu 't4{+ o Fh* ,t,f{

+L *o{o, l, {ns^ sh{L

I * = 5 + n

= + I f l r o { + TA o

T.^ oroli",n *{o havk- }vrax in,,t**\ ou {!ucf,u u, , +L

**" .xffe.t"o^ h*.ux *o lo-s gs,.r-fr*ot 'ni4;^1*r4*r.e,4 L-E

5 t = * h ' c * \

= ] \ - n , n * o , f , 2 -

+ d = ( a m - r ) + , o \ = 1 , 2 " . - -' 4h.

d = ( > * * l \ &' 4t1t

= (am-r r ) 9eqe 'n

4 (z :

= ( > r y 1 + \ ) ( 6 > . l n * ) f i a o , 1 , L . . _

trwu, &,nin i*o nw1 ,x$o*t;nn , $ d.uqbr^ch;ut ;^{zn(*,r**x

5 . t = c t - t ' n . A / h , f y ' = ( z m + t ) f i l d = o , f r z -

' 4rt t

= ) m ( b z . 9 n * ) * = t , z . " . *

o rF A = o r l p ) - - -

T.

I M

_\2

oftca' , -r!l l^4+k -1" a^ *fa '*t I

(o 'PL) " - ,+U '= J , ( t

\ \ ( op l ) -p^n ,

. ' =

l n . t \ \ { " t l e t t l

.t

+t oyl icol po+ !,, o{,#-era,^raI I t t' oPD

= (op l ) f , ^ r r (opL )^ .n+6

?- Jn,Q. a,{

{" n^*h*r "fah.k # , \u )

+C,"+," ,

= J f u l l / -

$;,4o' AJ ( ,'n./* al,'Z br;6h1 ̂^ol

Vrn- t ) lN : ) T = $ ( n - t ) +z\

l + A = l . o o o 3 , 1 * = o . l n a

N = + ( t " o o o 3 - t ) t o . t \

9 ? o X / o - 9

h = ( ? o f 1 n ' l r n

= &o3#1

b)

a) F- . +,.r

I.lo,^, ,

i r

a* nrolw

1uo o sfif saTi hX- { t s

&xtra GPD i^lw6sol

s ' = n { ' o (

*p ca ne.e I tl;g

V i : ! = n +N D / \

x = - h d - P =h

= lr. k aw\

A X

-\

OPD

Yor"g ;,rf *,rlorc,n a.

:p.h

h = \D " : {dooxto-lJcVLa x f o . o o ! )

= f . 2 r l1h4

*,'fh +l* ,r*{sr;ol

uff +L *^1r*,'ol

1llu[J n=,.,

o[ =o.oh",^

,{ +k!

S =

+kr

is

+*

y{.ax o

Aof $,f*t" *

- ( { .F}( o.€Xr; }Jzt( t . t r r o - t )

6i l*..1.f\

l^'thfr 'f &t*

+ a K

f ^ l r{ c m

aoPD =

\ t -e a (

o . o I

AX

a n[ax) "1. = A

J. t€xt ;1 , - -a( 1,3+) ( 8.Bxlo-s)

" z r d , o r 0 . o f 3 o

tA" DPD +.o\ +Lo lEt

EFD* =

-$. o,d,)a.uen{- +;,)T"s , 4hit^ oHo gh'"il r "t**! 1od^dr {2+h

- u= 3 . g x t o

' h n

+t- {* o t'.-t,,.'/ie r*${utuA4,..d ,l o. / r ur-iLe L ,

).n d^

) n X 'n * ind

Q. n 7^ c( $, s* l lJ

ol t{fn cn"r ,(a& yt,*l

NZfi ax

e . I X l e - 9

C:\Docs\MOptics\HW\HW4\prob7_1.mAugust 1, 2005

Page 110:24:49 PM

% 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']);

C:\Docs\MOptics\HW\HW4\prob7_2.mAugust 1, 2005

Page 110:28:13 PM

% 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']);

0 2 4 6 8 10 12 14-6

-4

-2

0

2

4

6

0 2 4 6 8 10 12 14-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Part 1

Part 2