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Interference and Diffraction
Spring 2020, Distance Lab 6
Interference and Diffraction
INTRODUCTION
This week, we’re investigating the wave nature of light. Specifically, the diffraction patterns of
bright and dark fringes that are formed when light passes through small slits.
We’ll need the following equations. First, for the multi-slit case:

where is the order number with 0 at the center, is the wavelength, is the distance between
the slits,
is the distance between the central bright fringe and the

bright fringe, and is the
distance from the slit to the screen, and for the single-slit case

where is width of the slit. Remember that for both of these, we’re making use of the small angle
approximation: because the angle
between each of the bright fringes we’re looking at and the
central fringe is very small, 

. Additionally, with the single slit we want
to know the width of the central bright fringe, which is wider than all the others. We can find that
as


Also don't forget, there is a recitation due this week. Please submit it separately in Blackboard,
to the appropriate assignment!
This week is the last lab! Thanks for hanging in there to the end of the semester.

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Interference and Diffraction
Spring 2020, Distance Lab 6
PRE-LAB VIDEO
Check out the video that we posted on Blackboard for getting started with the concept of the wave
nature of light, specifically interference and diffraction. It’ll define all the variables for you to get
you ready for the week.
https://brockport.open.suny.edu/bbcswebdav/pid-1478066-dt-content-rid-
10793587_1/courses/202002-XLSDE/DoubleSlitPreLab.mp4
LAB VIDEO
Check out the video for this experiment. It’s important, and you probably won’t be able to do the
lab without it! https://youtu.be/NOtiixRhi4I.
DATA ANALYSIS GUIDE
Having recorded pictures of our diffraction patterns, now we want to analyze those to extract
and calculate the wavelength of the laser with the double slit. If you grab images.zip from
Blackboard, you’ll see that the image filenames tell you what and are. You’ll need those, so
make sure to record them. Note that the slit separation and width is very small, you probably
couldn’t see them at all in the lab video!
It’s up to you how you want to measure
. I made vertical lines in MS Paint! Just be consistent
in your approach.
QUESTION 1: USING THE DOUBLE SLIT IMAGE, MEASURE AND RECORD
TO THE RIGHT AND
THE LEFT SIDE OF THE CENTRAL FRINGE. START WITH FINDING THE OFFSET, THEN THE
POSITIONS OF THE FRINGES.
Offset of the central fringe from zero = ___0.1__ cm

= 0.6 cm
corrected

= 0.6-0.1 = 0.5 cm

= 0.4 cm
corrected

= 0.4+0.1 = 0.5 cm

= (0.5+0.5)/2 = 0.5 cm
Hint for the correction: if the central fringe position is , the corrected value is  . If 
  and  , the corrected value is 0.4 cm.

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Interference and Diffraction Spring 2020, Distance Lab 6 Interference and Diffraction INTRODUCTION This week, we’re investigating the wave nature of light. Specifically, the diffraction patterns of bright and dark fringes that are formed when light passes through small slits. We’ll need the following equations. First, for the multi-slit case: 𝑚𝜆 = 𝑑𝑥𝑚 , 𝐿 (1) where 𝑚 is the order number with 0 at the center, λ is the wavelength, 𝑑 is the distance between the slits, 𝑥𝑚 is the distance between the central bright fringe and the 𝑚th bright fringe, and 𝐿 is the distance from the slit to the screen, and for the single-slit case 𝑚𝜆 = 𝑎𝑥𝑚 , 𝐿 (2) where 𝑎 is width of the slit. Remember that for both of these, we’re making use of the small angle approximation: because the angle θ𝑚 between each of the bright fringes we’re looking at and the central fringe is very small, sin θ𝑚 ≈ tan θ𝑚 ≈ 𝑥𝑚 /𝐿. Additionally, with the single slit we want to know the width of the central bright fringe, which is wider than all the others. We can find that as width = 2λ𝐿 . 𝑎 (3) Also – don't forget, there is a recitation due this week. Please submit it separately in Blackboard, to the appropriate assignment! This week is the last lab! Thanks for hanging in there to the end of the semester. Interference and Diffraction Spring 2020, Distance Lab 6 PRE-LAB VIDEO Check out the video that we posted ...
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