Studio Session 10

Diffraction and interference

imageWhen monochromatic light from a distant source passes through a narrow slit of width w in an opaque mask we observe a diffraction pattern on a distant screen.  The pattern is characterize by a central maximum and alternating dark and bright fringes, which appear symmetrically in both sides of the central maximum.  The central maximum is twice as wide, and much brighter than the other bright fringes.

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The dark fringes in the diffraction pattern of a single slit are found at angles θ for which w sinθ = mλ, where λ is the wavelength of the light and m is an integer, m = 1, 2, 3, ... .

imageThe intensity at the screen is proportional to the square of the electric field amplitude. 

What if we remove the mask and only leave the blocker of width w?  Using Huygens' principle we have

Emask with slit + Eblocker (no mask) = Enon-diffracted beam.

Here Emask with slit is the field produced by sources at locations of the mask and Eblocker (no mask) is the field produced by source at locations of the blocker.
Therefore

Eblocker (no mask) = Enon-diffracted beam - Emask with slit.

For a laser beam the divergence angle θ0 is small, and for angles θ > θ0 we have

Eblocker (no mask) = - Emask with slit.

For angles θ > θ0 the average intensity, which is proportional to the square of the electric field, therefore is the same as that for the single slit.  Dark fringes in the diffraction pattern are found at angles θ for which w sinθ = mλ.


imageIf light with wavelength λ passes through two or more slits separated by equal distances d, we will observe interference fringes inside the single slit diffraction pattern.  At certain angles we observe constructive interference.  These angles are found by applying the condition for constructive interference, which is

d sinθ = mλ, m = 0, 1, 2, .

We will only see the bright interference fringes, if they do not appear at the angle θ of a diffraction minimum.  If d sinθ  = mλ = w sinθ, then the bright fringe of order m will be missing.


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imageIn this session you will use a helium-neon (HeNe) laser to determine the number of grooves per mm of a diffraction grating, to measure the distance d between adjacent wires and the width w of the gap between the wires of 2-dimensional wire mesh, and to measure the width of a human hair.

Open a Microsoft Word document to keep a log of your experimental procedures, results and discussions.  This log will become your lab report.  Address the points highlighted in blue.  Answer all questions.

Equipment needed:


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Experiment 1

imageUse the equipment provided to determine the number of grooves per mm of a diffraction grating.

Record all your measurements and calculations and results in your log
Discuss and comment on your results.  Did anything surprise you?


Experiment 2

imageUse the equipment provided to measure the width of a human hair.

Record all your measurements and calculations and results in your log
Discuss and comment on your results.  Did anything surprise you?


Experiment 3

imageUse the equipment provided to measure the distance d between adjacent wires and the width w of the gap between the wires of 2-dimensional wire mesh.

Record all your measurements and calculations and results in your log
Discuss and comment on your results.  Did anything surprise you?


Convert your log into a session report, certify with you signature that you have actively participated, and hand it to your instructor.