1. Interference by multiple beam reflections: Newton’s Rings
Aim:
1. Studying the interference phenomenon due to multiple reflections of light
waves from gradually varying air film.
2. Determination of the wavelength of a monochromatic light using Newton’s
rings.
Apparatus: Plano – convex or bi - convex lens, monochromatic light (sodium or
laser light), traveling microscope, spherometer.
Theory
When a plano-convex lens with its convex surface is placed on
a plane glass sheet, an air film of gradually increasing thickness
outward is formed between the lens and the sheet. The
thickness of film at the point of contact is zero. If
monochromatic light is allowed to fall normally on the lens,
and the film is viewed in reflected light, alternate bright and
dark concentric rings are seen around the point of contact. These rings were first
discovered by Newton, that's why they are called NEWTON'S RINGS.
When monochromatic light is incident on a thin film of refractive index n
confined between two dielectric surfaces (glass, for instance), then part of the
light will be reflected at the upper surface and part of it will be refracted to the
lower glass surface where it undergoes multiple reflections before being able to
transmit back to the upper surface as illustrated in figure 1. Thus, at the upper
surface there will be two kinds of waves:
I. Waves that reflect directly at the upper optically denser medium to a lower
optical density medium (light ray 1). Here, the reflected wave undergoes a
phase change of 180o on reflection.
II. In this kind, the waves undergo either one internal reflection (light ray 2) or
many of this reflections
Light Beam Reflected light Beam
(light rays 3,4,5,…) prior no 1 2 3 4 5
to being refracted to the
lesser optical density
medium. n
If the film thickness is d and of
refractive index n, and the
light is allowed to incident
normally to the film, the Figure 1 Transmitted Light Beam
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2. Interference by multiple beam reflections: Newton’s Rings
optical path difference between any two rays is given by:
Rays 1, 2, 3, 4, … may interfere and interference fringes will be viewable if the
reflected rays are converged by a convex lens.
Newton discovered that interference fringes may also be generated by an air film
of varying thickness (i.e., the two surfaces confining the air film are not parallel).
For an air film of varying thickness to be formed, a convex or Plano – convex lens
is laid over a plane glass plate G, figure 2. Using a thin glass sheet inclined at 450
angle with respect to the incident light beam, i.e., with the horizon, part of the
rm
R
R
1 2
M
R-dm
L
L rm do
dm do+ d
G G
T T
Figure 2: creating Newton’s Rings
light will be reflected towards the air film. When a light ray is incident on the
upper surface of the lens, it is reflected as well as refracted. When the refracted
ray strikes the glass sheet, it undergoes a phase change of 180O on reflection.
When looking to the light rays reflected from both the lens L and the glass plate G
through the eyepiece of a traveling microscope focused at the glass plate G,
successive dark and bright concentric circular fringes “Newton’s rings” occur
through monochromatic light interfering in the thin intermediate film between a
convex lens and a plane glass plate. Ray 1 reflected at the underside of the lens
thus interferes with ray 2 reflected at the top of the glass plate.
The film of air at a distance r from the point of contact between the lens and the
glass plate has a thickness D = d ± do. As ideal contact is not present, we must take
do into account. do is positive when, for example, there are particles of dust
between the lens and the glass plate, but is can so also be negative when the
pressure is greater. In either case, the central may be bright or dark of unknown
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3. Interference by multiple beam reflections: Newton’s Rings
order of interference. On the other hand, if the pole of the lens is in intimate
contact with the glass block, then the central fringe will be dark of order of
interference m=0. The geometrical path difference of the interfering rays is
therefore:
In addition, the ray reflected from the plane glass surface experiences a phase
shift always occurs when light travels from the optically thinner towards the
optically denser dielectric medium and is partially or totally reflected at the
interface. The effect of this corresponds to a distance travelled of length . In
all, therefore, there is an apparent path difference, therefore:
The optical path difference between the two – type reflections:
For the interference rings of maximum cancellation, i.e. dark fringes, the optical
path difference equals even multiple of , thus:
Or
In accordance with Figure 2, and using simple trigonometry, a relation between
the radius rm of the mth dark ring, the thickness d and the radius of curvature R of
the plano-convex lens (in the ideal case do = 0) may be derived. Thus:
In case of slightly convex lenses, , so that may be neglected and the
previous equation becomes:
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4. Interference by multiple beam reflections: Newton’s Rings
Thus, the thin film thickness dm may be given in term of the mth ring radius rm (or
diameter Dm) as follows:
Therefore, the conditions for the dark and bright interference fringes will be:
Like the Haidinger fringes, Newton’s rings are also circular, but the two differ at
the fundamental level. The center of the Haidinger fringe pattern is occupied by
the fringe of the highest order which may be bright, dark, or may have any
intermediate intensity. The center of the Newton’s ring pattern in reflected light
always has a dark fringe of the lowest order. It is somewhat puzzling why these
fringes are named after Newton since Newton was not a believer of the wave
theory of light.
For the evaluation, is plotted against m. The wavelength of the transmitted
light is obtained from the slope of the straight line:
In the set-up
Figure 3: Radius of the interference
described, the rings as a function of the
Newton’s rings are order number.
observed in
transmitted light.
The interference
rings are
complementary to
those in reflected
light. In the latter 0 m
case, therefore, the
light rings are counted and not the dark ones.
Procedure
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5. Interference by multiple beam reflections: Newton’s Rings
1. The experiment is set up by putting the plano – convex lens over the glass
plate. Both the lens L and the glass plate G should be thoroughly clean and
dust – free.
2. The traveling microscope is focused on the glass plate. To achieve this, a
paper with a mark may be placed over the glass plate and the traveling
microscope is moved up and down till getting a sharp and distinct image of
the mark in the eyepiece field of view.
3. The 450 angled beam splitter glass plate is illuminated with a
monochromatic light (sodium light or any other coherent light).
4. Doing so, Newton’s rings should now be viewable at the focal plane of the
traveling microscope’s eyepiece. The ring pattern may not be extremely
sharp and, thus, blurred. This problem can be easily overcome by adjusting
focusing the traveling microscope eyepiece relative to the plano – convex
lens since it was focused on the glass plate.
5. Before measurements are to be taken, its important to insure that the
central spot is dark and not bright!! Why?
6. Measurement of the radius (or diameter) of a suitable set of successive
rings is to be done by recording the vernier reading after making the
eyepiece’s cross hairs at the right and left sides of each dark interference
ring. Its advisable to start taking the measurements from the left – hand
side of say, the 5th dark ring, and keep moving the traveling microscope in
the same direction, i.e. to the right – hand side. This is essential to avoid the
backlash error.
7. The radius of curvature of the plano – convex lens can be calculated by the
spherometer.
8. A graph of is plotted against m. The wavelength , in nm, of the
transmitted light is obtained from the slope of the straight line.
Microscope’s Venire Microscope’s Venier Ring Radius
Ring Order mth Ring Radius
Reading Reading Squared
m rm cm
XR cm XL cm r2m cm2
5
4
3
2
1
Discussion
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6. Interference by multiple beam reflections: Newton’s Rings
1. What are the coherent sources generating the ring interference pattern?
How about their types (real, virtual, one real and the other virtual)?
2. Is the pattern central spot dark or bright? Why? Write down its equation
giving explanation to your choice of the equation.
3. If the interference rings were not circular in shape and deformed, what
would the reason for this be? How can it be fixed?
4. Why are the interference fringes circular instead of being straight?
Confirming the answer with mathematical equation will be credited.
5. Show with schematic diagram how the current experiment can be modified
to measure the refractive index of a fluid (liquid or gas). How will the final
formula look like?
6. Does the interference pattern change upon using a lens of higher radius of
curvature? Illustrate how the diameters of the interference rings will be
affected. Confirming the answer with mathematical equation will always
be credited.
7. Newton’s rings are observed with a 10 m radius of curvature plano-convex
lens resting on a plane glass plate. (a) Find the radii of the dark interference
rings of the various orders observed by reflection under nearly
perpendicular incidence, using light of wavelength 4.8 10-7 m. (b) how
many rings are seen if the diameter of the lens is 4 cm?
8. Why is it so much easier to perform interference experiments with a laser
than with an ordinary light source?
9. A lens with outer radius of curvature R and index of refraction n rests on a
flat glass plate. The combination is illuminated with white light from above
and observed from above. Is there a dark spot or a light spot at the center of
the lens? What does it mean if the observed rings are noncircular?
10. A plano-concave lens having index of refraction 1.50 is placed on a flat glass
plate. Its curved surface, with radius of curvature 8.00 m, is on the bottom.
The lens is illuminated from above with yellow sodium light of wavelength
589 nm, and a series of concentric bright and dark rings is observed by
reflection. The interference pattern has a dark spot at the center,
surrounded by 50 dark rings, of which the largest is at the outer edge of the
lens. (a) What is the thickness of the air layer at the center of the
interference pattern? (b) Calculate the radius of the outermost dark ring.
(c) Find the focal length of the lens.
11. In a Newton’s-rings experiment, a plano-convex glass (n = 1.52) lens having
diameter 10.0 cm is placed on a flat plate. When 650-nm light is incident
normally, 55 bright rings are observed with the last one right on the edge of
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7. Interference by multiple beam reflections: Newton’s Rings
the lens. (a) What is the radius of curvature of the convex surface of the
lens? (b) What is the focal length of the lens?
12. Are Newton’s rings obtainable with the transmitted light beam of figure 1?
13. Why does not the straight line in figure 3 pass through the origin?
14. When is the presence of the 450 angled beam splitter glass plate not
necessary?
15. A plano-convex lens having a radius of curvature of R = 4.00m is placed on
a concave glass surface whose radius of curvature is R =12.0 m. Determine
the radius of the 100th bright ring, assuming 500-nm light is incident
normal to the flat surface of the lens.
16. Does a phase shift of π occur when light travels from the optically thinner
towards the optically denser metallic medium?
17. What is meant by “fringe of equal inclination”, “fringe of equal thickness”?
18. In the current experiment, does light behave like a particle (photons) or
like a wave or both?
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