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CAUTION : Never Look Directly At The Light From A Laser
44
PRINCETON UNIVERSITY
PHYSICS 104 LAB
Physics Department
Week #10
EXPERIMENT IX
PHYSICAL OPTICS (Interference and diffraction)
This is the second week of experiments on the behavior of light - last week we adopted the
simplistic but useful assumptions of ray optics. We ignored completely that light travels from one
place to another as a wave; a short wave, but a wave nevertheless.
This week we shall:
repeat Youngs double slit experiment, (which works only because light does behave
like a wave,) and get a rough measurement of the wavelength of the laser light.
explore the behavior of light waves passing through a number of double slits each
with a different distance (d) between the slits.
explore the behavior of light waves passing through a number of single slits, each with
a different width (a), and a circular aperture.
explore the behavior of light waves that pass through a multi-slit grating each with a
different number of slits (n).
use a high quality multi slit replica grating with 750 slits per mm. to make a rather
precise determination of the wavelengths of the three visible spectral lines in
hydrogen (the Balmer series, the lines on which Bohr based his theory of atom).
Because of the very small wavelength of light, diffraction and interference are most easily
seen with very small apertures, and therefore, with a bright light. In much of what follows we
shall be using a special mask, and a laser.
CAUTION : Never Look Directly At The Light From A Laser
Laser light is very bright and focuses to a very small spot on the retina, possibly causing
permanent damage.
1) Youngs Double Slit Experiment
In this section, you will make a double slit and use it to measure the wavelength of light
from a laser.
CAUTION : Never Look Directly At The Light From A Laser
You have a small piece of exposed photographic plate. Look at the reflection from each
side and find the side with the black emulsion on it. You also have a pair of razor blades taped
together, and a straight-edge. Place the straight-edge on the emulsion side of the glass plate. 45
Holding the double razor blade between your middle finger and thumb, with your fore finger
pressing down on top (the dull part), draw a line on the photographic plate parallel to one edge
and about 0.5 cm in from one edge. Look at it with a magnifier to see if there is a clean double
line scratched in the emulsion. If it is less than ideal, try again near the other edge. A third try
can be made near the middle of the plate, if needed.
The spacing between the lines can be easily measured by measuring the thickness of the
two razor blades with a micrometer caliper. Assuming that the grounded tapers on the razor
blades are alike, the spacing of the lines is just the thickness of one blade (half the thickness of
two).
Mount your double slit in a spring clip in front of the laser, with the slits horizontal.
Mount the metal plate screen with the millimeter scale at the other end of the optical bench.
Carefully adjust the height of the slits until the laser beam is centered on them, producing a
Youngs pattern on the metal plate screen. Measure the spacing between maxima on the scale.
You should try to include a large number of maxima in the measurement so that you can measure
the distance between them and divide by the number of intervals to get better accuracy. Also
measure the distance from the slits to the screen.
The angle between adjacent maxima in Youngs pattern is given by :
d
Sin =
where d is the separation of the slits. This gives the wavelength of the laser. Compare your result
with the accepted value of the wave-length of the laser light you are using
(
= 632.8 nm). There
may be as much as a 10% error due to asymmetric grinding of the edges of the razor blades.
Write your result in the space provided on the blackboard. We shall arrive at a class value and an
uncertainty bar by finding the average and the standard deviation of the measurements of the
individual groups.
Diffraction
Mount the Helium-Neon Laser (
=
632.8 nm),
the Slit-film Mask, and the gridded screen (to
catch the diffracted light) on your optical bench.
The mask has many different patterns; they are
shown schematically in the figure on the right.
The code at the side of each set of slits indicates
the pattern. Top # = # of slits. Center # = width
of slit (
×
4.4
×
10 3
cm). Bottom # = slit
separation (
×
4.4
×
10 3
cm). For example, pattern
A-3 (15, 1, 3) implies 15 slits each of width 4.4
×
10 3
cm, and separation of 13.2
×
10 3
cm.
between slits. The widths are only approximate.
Believe your data.
15
1
3
30
1
1
80
.25
.5
40
.5
1
20
1
2
A
B
C
D
E
1
32
-
1
16
-
1
8
-
1
4
-
1
2
-
1
2
-
1
16
-
1
1
-
1
1
-
2
1
2
3
1
2
4
1
2
10
1
2
1
2
-
2
2
2
2
2
6
2
2
14
2
2
30
1 2 3 4 5 46
2) Complete your look at Youngs double slit pattern by observing the patterns gotten by shining
the laser onto the screen through a series of double slits with increasing distance (d) between slits
5B, 5C and write down what you observe. You need not make any measurements or calculations,
just draw the patterns in your notebooks and write down your qualitative observations.
3) Diffraction by a single slit.
A single slit, width (a), also has an interference pattern on a distant screen, because of interference
between light coming from one part of the slit and light coming from another.
In this pattern :
Minima appear at such that a sin


= m


m = 1, 2, 3, ...
Look at the single slit diffraction pattern by shining laser through a series of single slits of
decreasing width --- 1C, 1D, 1E, and observing the pattern on the screen --- What happens to the
pattern on the screen as you move from 1C to 1E? Once again draw the patterns in your notebook
and write down your observations.
3A) Diffraction by a Round Aperture
Make a tiny, neat, round pinhole in a piece of aluminum foil by smoothing it over a piece
of Lucite (or the bench) and firmly pressing a sharp sewing needle down on it. Remove the
needle before lifting the foil from the Lucite.
Place the pinhole close in front of the laser and observe the diffraction pattern on the
screen. Make a measurement of the diameter of the first dark ring and calculate the diameter of
the pinhole, knowing the wavelength. The relationship for circular geometry is:
sin

= 1.22 ( /a)
where a is the diameter of the hole, and is the angle from the center to the first dark ring.
The factor of 1.22 comes from the Bessel functions needed to analyze the circular geometry.
4) Multi-slit diffraction.
A multi-slit, i.e. n identical slits, each separated from the next by distance (d) has the
remarkable property that as the number of slits (n) increases, the maxima occur just exactly when
the maxima of the double slit appeared, except the maxima become brighter and brighter, and
narrower and narrower. These maxima are called the primary maxima :
For multi-slit diffraction maxima appear at such that d sin


= m


m = 0, 1, 2, 3, ...
More and more secondary maxima appear between the principal maxima as n goes up, but
they have less and less importance as the number of slits (n) is increased.
Observe the patterns 4B, 4C, 4D, 4E, 3E, in which the number of slits increase from 2 to
20 with the same slit width and separation. How does the pattern change as you increase the
number of slits? Draw the patterns in your notebook and write down your observations. 47
5) Use the multi-slit diffraction
grating (the 35mm slide) to
measure the wavelengths of light
using the apparatus shown at the
right. Get warmed up for your
measurement of the wavelength of
the three visible Balmer spectral
lines of Hydrogen, by measuring
the wavelength of two of the
brighter visible Mercury lines. Then
determine the wavelengths of the
three visible Hydrogen spectral
lines and record them --- also write
them on the board in the
appropriate column.
As remarked before, the relationship that governs is: d sin


=



(in the first order)
The grating you are using has 750 lines (slits) per millimeter.
The apparatus is so clearly self-explanatory that your TA will only explain it to you if you cant
figure it out yourself --- the main difference from what you have already been doing with light
passing through holes of various shapes, and a pattern on a screen, is that this time you look
through the grating, as shown in the illustration.
Mercury Lines
(in the visible)
Wavelength
(nm)
Hydrogen Lines
(in the visible)
Wavelength
(nm)
yellow doublet
577 / 579
red
656
green
546
aqua
486
blue-violet
436
blue-violet
434
violet
405


your eye
grating and holder
meter stick
light source
slit
Spectral lines
View of the apparatus looking down from above