This document describes an experiment to determine the width of a sheet of paper using wedge interference phenomenon. A sheet of paper is placed between two glass plates, forming an air wedge. Monochromatic light is shone through the wedge, and interference fringes are observed in the microscope. The distance between fringes is measured and used to calculate the width of the paper based on the wedge angle and refractive index differences.

1. Determination of the width of a paper employing wedge interference
phenomenon
Aim: evaluating the width of a sheet of paper via wedge interference
phenomenon.
Apparatus: microscope glass slide, thick glass plate (opaque one is preferable),
traveling microscope, convex lens.
Theory
When a piece of paper of width t is introduced between the
edges of two transparent glass plates, a thin wedge – shape air
film will be formed as illustrated in figure 1. The
monochromatic light incident normally on the air wedge will
be divided into two parts by the wave amplitude – division
method. One part is reflected at the upper glass surface OP and
the other part passes to the lower glass surface OP’ where it undergoes a further
reflection upon striking that surface. Since this reflection is from an optically
denser (higher
refractive index) Traveling
medium (glass) to Microscope
a lower optical
Convex
density medium Lens
(air), the reflected
light waves will be 45
phase shifted by
180o (this is Glass
equivalent to an plate Coherent
additional optical Light Beam
path difference of P
B Sheet
between the Of t
two upper and A C Paper
α
lower reflected O A B’ P’
’
beams). Due to the y
overlapping ℓ
(interference) of
Figure 1: experimental set – up of air –
the two reflected wedge interference phenomenon
light beams, bright
and dark straight
fringes are observed in the traveling microscope’s field of view.
Wedge interference phenomenon page 1 of 4
Tuesday, May 22, 2012
Baghdad University – College of Science – Department of Physics – Optics Laboratory Administration Tele:
+009647702981421

2. The fringe at point A is formed by interfering light ray, reflected off the upper
glass surface OP, with the one reflected from the lower glass plate which suffered
a 180o - phase shift in addition to traversing double the distance AA’ when it
propagates back and forth. If the total phase shift equals odd multiples of half the
light wavelength, then a dark interference fringe will be formed. On the other
hand, the interference fringe will be bright whenever the total phase shift equals
even multiples of the light wavelength used. The next interference fringe formed
at point B is due to the increase of air – wedge width by an amount of half the
light wavelength (the distance BC in the figure 1).
If α is the wedge angle in degrees, then from the triangle ABC it is apparently that:
Where: y represents the distance between two successive (dark or bright)
fringes. In the triangle OPP’:
Where t=PP’ represents the width of the paper in mm unit and is the
separation between the inner edge of the paper and line of contact of the two
glass plates.
Procedure:
1. A convex lens is used to get a parallel light beam emerging from the
monochromatic light source (typically the monochromatic sodium light
or any other coherent light source, for example He-Ne
laser light ). This parallel light beam is to be making -
angle of incidence with a horizontally oriented, - angle, half – silvered
glass plate. The light rays reflected off this plate will perpendicularly
incident on the lower thick glass plate of the air – wedge.
2. The traveling microscope is then focused until getting the lower thick glass
plate of the air – wedge at the focal plane of the traveling microscope’s
eyepiece. Doing so, a distinct interference pattern should become viewable.
3. The distance between a suitable number of dark (or bright) fringes is
measured using the traveling microscope vernier and the width of the dark
of bright fringe is deduced by dividing the measured distance on the
number of fringes. The measurement is then recorded in a suitable table.
Wedge interference phenomenon page 2 of 4
Tuesday, May 22, 2012
Baghdad University – College of Science – Department of Physics – Optics Laboratory Administration Tele:
+009647702981421

3. 4. Step 3 is repeated for a number of times and the average of such
measurements is evaluated.
5. Using a micrometer vernier, the distance is measured.
6. Finally, the width of the paper t is estimated by applying formula 1.
Discussion:
1. How is light behaved in this experiment?
2. What is the appearance of interference fringes formed in the air – wedge?
Why do they appear like this? Stating the mathematical equation is
preferable.
3. What is the type of interference fringe (i.e., dark or bright) formed at the
contact line of the two glass plates? How about its equation? Explain your
answer.
4. Does wedge interference phenomenon depend on wave front division or
wave amplitude beam splitting? State other experiments which depend on
the same operating principle.
5. Evaluate the optical path difference of the sixth dark fringe assuming that
the medium between the two glass plates is air once and water in the other
and the light source used is the sodium monochromatic light.
6. How can the air – wedge experiment be modified to measure the refractive
index of unknown liquid, for example water? How will the final formula
look like? Can you derive this formula? No doubt, you can!!
7. Point out natural daily phenomena in which multiple – reflection
interference is truly confirmed.
8. If sodium monochromatic light is replaced by polychromatic light (white
light for instance), will the interference pattern remain viewable? How will
the fringes look like? Why?
Wedge interference phenomenon page 3 of 4
Tuesday, May 22, 2012
Baghdad University – College of Science – Department of Physics – Optics Laboratory Administration Tele:
+009647702981421

4. “A candle loses nothing of its light in lighting another”.
J. K. Jibran
Wedge interference phenomenon page 4 of 4
Tuesday, May 22, 2012
Baghdad University – College of Science – Department of Physics – Optics Laboratory Administration Tele:
+009647702981421