Phys 23 T10 Thin Film Interference

8/10/2019 Phys 23 T10 Thin Film Interference

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EXPERIMENT 10

THIN FILM INTERFERENCE

Light from a monochromatic source is shined downward on two glass plates that areseparated at one end by a hair. Light that is reflected from the top and bottom surfaces of thewedge-shaped thin film of air undergoes interference, and a series of dark and light lines are seen.By counting the number of dark or light lines over a known distance, measuring the length of theglass plates, and knowing the wavelength of the monochromatic light, the thickness of the haircan be found.

THEORY

Suppose monochromatic light is incident on a thin film of thickness t and having an index ofrefraction n. Part of this light reflects back toward the observer from the top and bottom surfacesof the thin film toward the observer, and part is transmitted through the thin film. !efer to "igure#.$

"igure #. %onochromatic light shown reflecting off the top and bottom surfaces of the thin film. &he transmitted light is not shown.

&he light leaving the source is in phase. 'owever, upon reflecting from the thin film back tothe observer, the light will necessarily be out of phase due to the extra distance ray B travels as itreflects off the bottom surface of the thin film. (f the light hits the surface perpendicularly oralmost perpendicularly, then the extra distance ray B travels is twice the thickness of the thin filmat the point where the light is incident. &his extra distance and the corresponding phasedifferences are related to each other as

#) - #


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phase difference * path difference ,

+ wavelength with in the thin film #$or

,+

+ n

t

= +$

where is the phase difference, t is the thickness of the film, and nis the wavelength of the lightin the thin film. (n this case, the thin film has an index of refraction n and n* n, where is thewavelength of the light in air. uation +$ then becomes

,+

+

t= /$

(f two waves interfere and the phase difference between them is 2m, where m * ), #, +, ...,then constructive interference results. 0nd, if the phase difference is +m 1 2$, where m * ), #,+, ..., then destructive interference results. 3ther phase differences give partial constructive ordestructive interference.

4hen the phase difference, , in /$ is replaced by the values of the phase difference, theresults are

mt =+ . ,...+,#,)=m 5$

for constructive interference, and

,

+

#+

+= mt ,...+,#,)=m 6$

for destructive interference.

0n added complication arises in thin film interference. (t is found that when light traveling in

a medium of one index of refraction is reflected from a surface of higher index, a -phase shiftoccurs. 7o phase shift occurs at the surface when the reflecting surface has a lower index ofrefraction. &he result is that if the total number of phase shifts that rays 0 and B undergo is 8eroor an even number, then 5$ and 6$ hold as above. But, if an odd number of phase shifts occur,then 5$ corresponds to destructive interference and 6$ corresponds to constructive interference.&hat is,

mt =+ . ,...+,#,)=m 9$

for destructive interference, and

#) - +


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,+

#+

+= mt ,...+,#,)=m :$

for constructive interference.

"or a wedge-shaped film of air between two glass plates a total of one phase shift occurs, so9$ and :$ are the appropriate expressions. 0 single phase shift occurs at the bottom surface ofthe thin film of air, but no phase shift occurs at the top surface. ach value of m in 9$corresponds to a dark line and in :$ a bright line. 4hen m = ) in 9$, this indicates that thethickness of the film is 8ero t * )$,so m = ) corresponds to the dark line produced at the point ofcontact between the two glass plates. &he next dark line away from the point of contact is m * #,and so on.

(n this experiment a wedge-shaped layer of air between two glass plates is produced byseparating one end of the glass plates with a hair. !efer to "igure +.$ 4hen monochromatic lightis shined on the plates from above, a series of bright and dark lines are seen. (n "igure + the

bright and dark lines are indicated by the letters B and ;, respectively.

"igure +. 0 side view of the thin film of air. &he distance between the linesand the thickness of the film are greatly exaggerated.

(f the number of dark lines are counted over a known distance d. similar triangles can beused to find the hair thickness &. &hat is, in the triangle P

.L

T

PR

QR

= =$

But QR =tt+N- ttwhere ttis the thickness of the film at the ith

dark line, tt>7is the thickness of

the film at the i +7$th

dark line, and P! * d. ?sing 9$ and setting % * t+7 then setting m *tand subtracting,

#) - /


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( ),

+++

NiNittQR tNt =

+== + @$

whereN is the number of dark lines in the distance d. uation =$ then becomes

.+ d

LNT

= #)$

APPARATUS

o sodium light source o blank paper o two plane, parallel glass plates o ruler o micrometer o #) cm focal length lens

PROCEDURE

a$ Alean the surfaces ofthe two glassplates and handle them so that no smudges are lefton their surfaces.

b$ Plug in and turn on the sodium light source.

c$ Aarefully draw two parallel lines one centimeter apart on the notebook paper. &his is

the distance d.!ecord d and the uncertainty, d.

d$ !euest a hair from the head of a member of your group and measure the diameter ofthe hair with the micrometer. !ecord this value and its uncertainty. Be sure not tocrush the hair when you tighten the micrometer.$

e$ Aarefully place the hair between the two glass plates perpendicular to the length of theplates and close to one end. ;o not press the plates together this will crush the hair.

f$ Lay the plates down over the lines drawn on the notebook paper so that the length ofthe plates is perpendicular to the lines. %easure the distance from the point of contact

of the glass plates to the position of the hair. !ecord the value L and its uncertainty, L.

g$ 0dCust the position of the sodium lamp until the light from the lamp shines almoststraight downward on the glass plates. 7otice the bright and dark interference lines.

h$ ?se the #) cm focal length lens as a magnifying glass and count the number of dark linesbetween the one centimeter marks on the notebook paper. !ecord the number of lines,

7, and the uncertainty in the count, 7.

#) - 5


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i$ 'ave each person in the group repeat steps d$ and h$ for his or her own data.

ANALYSIS

&he uncertainty in the thickness of the hair due to uncertainties in measurements is

,

++=

d

d

L

L

N

NTT

##$

where the wavelength of the sodium light is assumed to be exactly 6=@ nm and the index ofrefraction of air is #,))).

Aalculate the thickness of the hair from #)$ and its uncertainty from ##$. !eport these

values and the value obtained from the micrometer reading in a table. 0lso graph these values on aone-dimensional graph.

QUESTION

#. (t is hard to get the bars to be parallel in this experiment. xplain why the bars tend to beso wiggly.

+. xplain why it is necessary to use a special sodium vapor lamp for this experiment ratherthan an ordinary white lamp.

/. xplain how the number of bars to be counted would be affected if the lamp were changedto a different source producing red light. 4ould this make the uncertainty in theexperiment smaller or greaterD

5. xplain why it is better to place the hair as far as possible from the contact point of theglass plates.

6. 'ow would dust and oil on the glass plates affect the resultsD

9. 4hat percentage error would result from miscounting the bars by oneD

:. 'ow would the data and results of the experiment be affected ff instead of glass we hadused a different transparent material for the platesD

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Phys 23 T10 Thin Film Interference

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