Sunday, April 15, 2012

How the wave Nature of light was first discovered

Strong evidence for the wave theory of light

interference-of-circular-waves

  First, we need to know:   Interference
  When two ball-ended dippers are attatched to the vibrator of the ripple tank, two sets of circular ripples are sent out which pass through one another as shown in the image.

  Where the two waves are superposed in the same phase, e.g., crest on crest, we get lines of increased disturbance or constructive interference. These are called the anti-nodal lines. In between these are the nodal lines along which the waves are exactly out of phase, e.g., the crests of one are superposed on the troughs of the other.
Here, provided the amplitudes of the two waves are the same, we now get zero resultant disturbance of the water surface, or destructive interference.

  A similar interference pattern is obtained if either a straight or a circular wave is incident on a vertical barrier having two small apertures. In this case, interference takes place between the emerging diffracted waves.

Tomas Young's experiment

  If we imagine that the two water waves sources to be replaced by two two point light sources then, if light is a form of wave motion, we should expect similar constructive interference to occur.
In other words we ought to get increased brightness along the anti-nodal lines and darkness along the nodal lines.

  At the beginning of the nineteenth century, Tomas Young did, in fact, perform such an experiment using the light diffracted from two pinholes and obtained a series of light and dark bands or interference fringes on a screen placed in the path of the light. This was very strong evidence for the wave theory of light.
Later he repeated the experiment using the light from two narrow parallel slits, with similar results.

interference-of-diffracted-waves

Production of interference fringes using Young's slits

  This image shows the general scheme of a modern version of Young's experiment.
Two very narrow, close and parallel slits S1 and S2 are illuminated by the light from a single slit S parallel to them, and placed in front of a strong monochromatic '= one color or wavelength' light source.

A sodium discharge lamp giving orange light is suitable, or alternatively, a white source may be used together with a color filter which transmits only a limited range of wavelengths.

Young's-slits-experiment

  The interference fringes can be seen by setting up a translucent screen and viewing from the side opposite to the slits. Tracing-paper makes a suitable screen. Otherwise they can be examined through a magnifying eyepiece.

  Note that the fringes are formed in space. They are said to be non-localized. Hence, light and dark bands will be formed on a screen placed anywhere in the fringe region and the spacing of the bands will increase as the screen is moved further from the slits.
The same applies when using a magnifying eyepiece which shows a section across the fringes in its image plane.

  The number of fringes seen depends on the width of the slits. The narrower the slits the greater will be the number of fringes, owing to the increased angular diffraction. They will, however, be much fainter since less light energy gets through.
The average wavelength of light is about 0.0005 mm.

  In order to pass sufficient light energy to give easily visible fringes, the slits have to be a good many wavelength wide. The angular diffraction of the light passing through them is, therefore, quite small.

The slit sources must be coherent.

  You may have wondered why it is necessary to have a single slit in front of the light source. The reason is that lamps do not emit light waves in the same regular manner as the dipper sends out water waves in a ripple tank.
The atoms in a light source give out millions of wave packets all with different phases and in different directions. If the single slit were not there the two slits would receive light from different parts of the source and so the light emerging from them would be in different and constantly varying phase. The function of the single slit is to cause the light to spread out over a cylindrical diffracted wavefront on which the phase remains constant. Thus, if the two slits are equidistant from the single slit they simultaneously receive light in the same phase.

If any sudden phase changes do occur in the light from the single slit, then the two slits will both be affected equally. In these circumstances the light from the two slits is said to be coherent.

  Tomas Young was well aware of this condition. One cannot obtain a constant interference pattern from two independent slit sources.

  Practical details. Good results will be obtained only if proper care is given to the presentation of the slits. One of the commonest methods is to use a pin to rule two parallel lines about a third of a millimeter apart on a piece of thin glass which has been coated with Aquadag 'colloidal graphite' and allowed to dry. The graphite is removed by the pin point, thus leaving two transparent slits. This is not as easy as it sounds: several trials may be necessary in order to obtain good slits.

  Good results are obtained by the following method.
A hole about 1 cm in diameter is made in a thin sheet of metal and, diametrically across it a short length of copper wire about 0.4 mm diameter is fixed with adhesive. To ensure straightness the wire should be cut from a length which has been stretched slightly by clamping one end in a vice and pulling the other end with piles. The slits are formed by sticking two pieces of razor blade on either side of the wire. This is best done under low-power microscope when it will be found comparatively easy to push the two pieces of blade into position to form two narrow, equal and parallel gaps before the adhesive sets. A pair of slits made in this way, about 0.06 mm wide and about 0.4 mm apart will, if used with a strong light source, give up to 18 fringes. Wider slits give fewer but brighter fringes.

  The single slit can be made by the same method, omitting the wire. It is, however, a definite advantage to use a variable slit if one is available, since its width can then be adjusted to give maximum brightness combined with good definition of the fringes.

  Needless to say, it is best to work in a dark room or at any rate in a dimly lit laboratory. When setting up the apparatus it is essential to see that the light source and single slit both lie on the perpendicular bisector of the line joining the two slits S1 and S2. If the fringes are poor, it will probably be due to lack of parallelism between the slits. A slight rotation of the slit S one way or other should bring about the desired results.

  More accurate results will naturally be obtained from micrometer measurements. The micrometer eyepiece has a vertical cross-wire on a horizontal slide which is moved by a micrometer screw. Readings are taken when the cross-wire is centered over the extreme fringes visible and from these the mean distance between adjacent fringes is calculated.

ray-diagram-young-experiment

fringes-and-wavelength

  To speak briefly:
For bright fringes : wave path difference = zero or an even number of half-wavelengths.

For dark fringes : wave path difference = an odd number of half-wavelengths.

Measurements of wavelengths from young's experiment

wavelength-calculation-experiment

  The image shows the ray geometry for the first bright fringe next to the central one.
The distance S2P is one wavelength longer than S1P. Thus, if we drop a perpendicular S1N 'not shown in the image' on the line S2P it will cut off a length S2N = γ. Bearing in mind the smallness of the distance d between slits and the fringe spacing x we may, to a very close approximation, regard the two bright-angles S2NS1 and PFB as equiangular and therefore similar.

Hence

γ/d =x/D

or

γ = xd/D

  The fringes are all effectively equidistant and so we take the fringe spacing as equal to the average spacing of as many fringes as can be seen and measured. It has already been explained how this may be done either with a micrometer eyepiece or, more roughly with half-millimeter scale used in conjunction with a magnifying glass.

  The distance d between the slits may also be measured with half-millimeter scale, though more accurate results are obtained with a traveling microscope. This microscope is fitted with a cross-wire on which the slits are focused in turn. The consequent movement d of the microscope carriage is measured by a vernier or micrometer screw.
Owing to the smaller percentage error involved, it is sufficiently accurate to measure the distance D with an ordinary millimeter scale.