In this laboratory students will use a HeNe laser to determine the number of grooves per mm of a diffraction grating and to measure the width of a human hair.
Background information:
(a) an opaque obstacle
When light from a distant source passes through a narrow slit of width a in a opaque mask the electric field at large distances is given by
E(θ) = (As/r0)cos(kr0-ωt)(sin(πa(sinθ)/λ)/(πa(sinθ)/λ).
and the average intensity is given by <I(θ)> = <I0>(sin2(πa(sinθ)/λ)/(πa(sinθ)/λ)2.
If we block the slit completely with an opaque blocker, the electric field at large distances is zero. If we remove the mask, the electric field at large distances is that of the non-diffracted beam
What if we remove the mask and only leave the blocker of width a? Using the Huygens principle we have
Emask with slit + Eblocker = Enon-diffracted beam.
Therefore
Eblocker = Enon-diffracted beam - Emask with slit.
For a laser beam the divergence angle θ0 is small, and for angles θ > θ0 Eblocker = - Emask with slit.
For angles θ > θ0 the average intensity, which is proportional to the square of the electric field, therefore is given by
<Iblocker(θ)> is proportional to (sin2(πa(sinθ)/λ)/(πa(sinθ)/λ)2.
Dark fringes in the diffraction pattern are found at angles θ for which a sinθ = mλ.
(b) a diffraction grating
If light with wavelength λ passes through a diffraction grating with grooves separated by a distance d, we will observe constructively interference at certain angles. These angles are found by applying the condition for constructive interference, which is
dsinθ = mλ, m = 0, 1, 2, ….
The experiment:
Equipment provided:
Procedure:
Use the equipment provided to determine the number of grooves per mm of a diffraction grating and to measure the width of a human hair. Make measurements for several orders of the diffraction pattern to obtain more accurate results.
Open Microsoft Word and prepare a report.
Summarize the experiment.
Briefly describe your experimental setup.
Present your results.
Comments?