M A M EL-Morsy
Optics II
Interference phenomena
17- NEWTONS'S RINGS
When a piano-convex lens of long focal length is placed on a plane glass
plate, a thin film of air is enclosed between the lower surface of ' the lens and
the upper surface of the plate. The thickness of the air film is very small at the
point of contact and gradually increases from the centre outwards. The fringes
produced with monochromatic light are circular. The fringes are concentric
circles, uniform in thickness and with the point of contact as the centre.
When
viewed
with
white
light,
the
fringes
are
coloured.
With
monochromatic light, bright and dark circular fringes are produced in the air film.
S is a source of monochromatic light at the focus of the lens L 1 (Fig.
8.25). A horizontal beam of light falls on the glass plate B at 45°. The glass
plate B reflects a part of the incident light towards the air film en closed by
the lens L and the plane glass plate G. The reflected beam from the air film is
viewed with a microscope. Interference takes place and dark and bright circular
fringes are produced. This is due to the interference between the light
reflected from the lower surface of the lens and the upper surface of the glass plate
G.
Theory. (i) Newton's rings by reflected light
Suppose the radius of curvature of the lens is R and the air film is of
thickness t at a distance of OQ = r, from the point of contact O.
74
M A M EL-Morsy
Optics II
Interference phenomena
Here, interference is due to reflected light. Therefore, for the bright rings
 2n
2  t cos  
Where
n = 1, 2, 3, ……
 1

(i )
2
etc.
Here  is small, therefore cos  = 1 and for air µ = 1
2 t 
 2n
 1

2
(ii )
For the dark fringe
2  t cos   n 
2t n
Where
n = 0, 1, 2, 3, ……
etc.
In Fig. 8.26
EP x HE  OE x  2 R  OE 
But
EP  HE  r , OE  PQ  t
and
2 R  t  2 R ( approximately )
r2  2 R t
t
r2
2 R
Substituting the value of t in equations (ii) and (iii), For bright rings
r2 
r 
2 n
 1  R
2
2 n  1  R
2
For dark rings
75
M A M EL-Morsy
Optics II
Interference phenomena
r2  n  R
n  R
r 
When n = 0, the radius of the dark ring is zero and the radius of
the bright rings is
R
. therefore, the center is dark.
2
Alternately dark and bright rings are produced ( Fig. 8.27).
Result. The radius of the dark ring is proportional to
(i)
n
(ii)

R .
and (iii)
Similarly the radius of the bright ring is proportional to
(i)
2n
1

2
(ii)

and (iii)
R
if D is the diameter of the dark ring
D 2r2
n  R
Example 8.46. A thin equiconvex lens of focal length 4 metres and
reflective index 1.50 rests on and in contact with an optical
flat, and using light of wavelength 5460 A, Newton's rings
76
M A M EL-Morsy
Optics II
Interference phenomena
are viewed normally by reflection. What is the diameter of the 5
th bright ring ?
The diameter of the n th bright ring is given by
2 2 n  1   R
Dn 
n  5 ,   5460 x 10 8 cm
f  400 cm ,
  1.5
 1
1 

 1 

R2 
 R1
R1  R , R2   R
1

f

2 
 1  
R 
1
2
 1.5  1 
400
R
R  400 cm
1

f
D

2 x 2 x 5  1 x 5460 x 10 8 x 400
 0.627 cm
Example 47. A piano-convex lens of radius 300 cm is placed on an optically
flat glass plate and is illuminated by monochromatic light. The
diameter of the 8 th dark ring in the transmitted system is 0.72
cm. Calculate the wavelength of light used.
Example 48. In a Newton's rings experiment the diameter of the • 15 th ring
was found to be 0.590 cm and that of the 5 th ring was
0.336 cm. If the radius of the piano-convex lens is 100 cm,
calculate the wavelength of light used.
77
M A M EL-Morsy
Optics II
Interference phenomena
Example 49. In a Newton's rings experiment, the diameter of the 5 th ring was
0.336 cm and Me diameter of the 15 th ring = 0.590 cm. Find
the radius of curvature of the piano-convex lens, if the
wavelength of light used is 5890 A.
Fig. 8.30
18- REFRACTIVE INDEX OF A LIQUID USING NEWTON'S RINGS
The experiment is performed when there is an air film between the planoconvex lens and the optically plane glass plate. These are kept in a metal
container C. The diameter of the n th and the (n + m) th dark rings are
determined with the help of a travelling microscope (Fig. 8.30):
78
M A M EL-Morsy
For air
Optics II
Interference phenomena
Dn2 m  4  n  m   R
Dn2  4 n  R
(i)
The liquid is poured in the container C without disturbing the
arrangement. The air film between the lower surface of the lens and the
upper surface of the plate is replaced by the liquid. The diameters of the n th
ring and the (n + m) th ring are determined.
For the liquid, 2  t cos   n  for dark rings
2  t n 
t 
but
2  r2
2 R
r2
2 R
 n 
n  R
r2 

D
2
4n  R
but r 
D2 

Example 50. In a Newton's rings experiment the diameter of the 10 th ring
changes from 1.40 cm to 1.27 cm when a liquid is introduced
between the lens and the plate. Calculate the refractive index of the
liquid.
Example 51. In a Newton's rings arrangement, if a drop of water (µ = 4/3) be
placed in between the lens and the plate, the diameter of the
10 th ring is found to be 0.6 cm. Obtain the radius of curvature
79
M A M EL-Morsy
Optics II
Interference phenomena
of the face of the lens in contact with the plate. The wavelength of
light used is 6000 A.
Example 52. Newton's . rings are formed by reflected light of wavelength 5895
A with a liquid between the plane and curved su rfaces. If the
diameter of the 5 th bright ring is 3 mm and the radius of
curvature of the curved surface is 100 cm, calculate the reflective-index
of the liquid.
Example 53. In a Newton's rings experiment the diameter of the 15 th ring
was found to be 0.590 cm and that of the 5 th ring was 0.336
cm. If the radius of the piano-convex lens is 100 cm, calculate
me wavelength of light used.
80
M A M EL-Morsy
Optics II
Interference phenomena
Example 54. In a Newton's rings experiment the diameter of the
12 th ring changes from 1.50 cm to 1.35 cm when a liquid is
introduced
between the lens and the plate. Calculate the refractive index of
the liquid.
D
   2
 D1
2

 1.5 
  
  1.235
 1.35 

2
19- INTERFEROMETRY
The phenomenon of interference has been used to test the planeness of
surfaces and also to reduce reflecting power of the lens and the prism
surfaces. Instruments based on the principle of interference of light are
known as interferometers. Michelson designed an interferometer to determine
the wavelength of light, thickness of thin strips and for the standardization of
the metre. The instruments designed by Jamin and Rayleigh are used to
determine the refractive index of gases and are known as refractometers.
20- MICHELSON INTERFEROMETER
Michelson interferometer consists of two highly polished mirrors M1
and M 2 and two plane glass plates A and C parallel to each other. The rear
side of the glass plate A is half silvered so that light coming from the source
81
M A M EL-Morsy
Optics II
Interference phenomena
S is equally reflected and transmitted by it. Light from a mono chromatic
source S after passing through the lens L, falls on the plate A. The lens L
makes the beam parallel. The plate A is inclined at an angle of 45°. One half
of the energy of the incident beam is reflected by the plate A towards the
mirror M 1 and the other half is transmitted towards the mirror M,. These two
beams (reflected and transmitted) travel along two mutually perpendicular paths
and , are reflected back by the mirror Al} and M 2 . These two beams return to
the plate A. The beam reflected back by MI is transmitted through, the glass
plate A and the beam reflected back by M 2 is reflected by the glass plate A
towards the eye (Fig. 8.37).The beam going towards the mirror M, and
reflected back, has to pass twice through the glass plate A. Therefore, to
compensate for the path, the plate i s u s e d between mirror M a nd A . T h e l i gh t
b e a m go i n g t o w a r d s the mirror M, and reflected back towards A also passes
twice through the compensation plate C. Therefore, the paths of the two rays
in glass are the same. The mirror M1 is fixed on a carriage and can be moved
with the help of the handle H. The distance through which the mirror M1 is moved
can be read on the scale. The planes of the mirrors M1 and M2 can be made
perfectly perpendicular with the help of the fine screws at tached to them.
The compensating plate is a necessity for white light fringes but can be
dispensed with, while using monochromatic light.
82
M A M EL-Morsy
Optics II
Interference phenomena
If the mirrors M1 and M2 are perfectly perpendicular, the observer's
eye will see the images of the mirrors M1 and M2 through A. There will
be an air film between the two images and the distance can be varied
with the help of the handle H. The fringes will be perfectly circular. If
the path travelled by the two rays is exactly the same, the field of view
will be completely dark. If the two images of M1 and M, are inclined (the
mirrors M1 and M2 not perfectly perpendicular) the enclosed air film, will
be wedge shaped and straight line fringes will be observed. When the mirror M 1 is moved away or towards the glass plate A with the help of the
handle H, the fringes cross the centre of the field of view of the observer's
eye. if M1 is moved through a distance X12, one fringe will cross the field
of view and will move to the position previously occupied by the next
fringe.
21- APPLICATIONS OF MICHELSON INTERFEROMETER
Michelson interferometer can be used to determine (i) the wavelength of a
given monochromatic source of light, (ii) the difference between the two
neighbouring wavelengths or resolution of the spectral lines, (iii) refractive index
and thickness of various thin transparent materials and (iv) for the measurement of the
standard metre in terms of the wavelength of light.
22-
DE T E R MI N AT IO N
OF
THE
WA VE L E N G T H
OF
MONOCHROMATIC LIGHT
The mirrors M1 and M 2 are adjusted so that circular fringes are visible in
the field of view (Fig. 8.37). If M1 and M 2 are equidistant from the glass
plate A, the field of view will be perfectly dark. The mirror M2 is kept fixed and
the mirror M 1 is moved with the help of the handle of the micrometer
screw and the number of fringes that cross the field of view is counted.
Suppose for the monochromatic light of wavelength, the distance through
which the mirror is moved = d and the number of fringes that cross the centre of the
d 
field of view = n. Then,
n
2 , because for one fringe shift, the mirror
moves through a distance equal to half the wavelength. Hence , can be
determined.
83
M A M EL-Morsy
Optics II
Interference phenomena
Example 55. In moving one mirror in a Michelson interferometer through a
distance of 0.1474 mm, 500 fringes cross the centre of the field of
view What is the wavelength of light ?
Example 65. Fringes of equal inclination are observed in a Michelson
interferometer. As one of the mirrors is moved back by 1
mm, 3663 fringes move out from the centre of the pattern.
Calculate .
Example 57 . In a Michelson interferometer 200 fringes cross the field of
view when the movable mirror is displaced through 0.05896 mm.
Calculate the wavelength of the monochromatic light used.
In a Michelson interferometer
84
M A M EL-Morsy
Optics II
Interference phenomena
Example 58. A shift of 100 circular fringes is observed when the movable
mirror of the Michelson interferometer is shifted by 0.0295
mm. Calculate the wavelength of light.
Example
59.
In
a
Michelson's
interferometer
200
fringes
cross
the
field of view when the movable mirror is displaced through 0.0589
mm. Calculate the wavelength of monochromatic light used.
Example 60. In a Micheleon's interferometer 100 fringes cross the field of view
when the movable mirror is displaced by 0.022948 mm. Cal culate the wavelength of the monochromatic light.
23- JAMIN'S REFRACTOMETER
It is used to determine the refractive index of a gas at different pressures. A and B are two glass plates silvered at their back surfaces. The two
plates are sufficiently thick and two identical glass tubes T1 and T2 are placed
.in the path of the beams 1 and 2 respectively (Fig. 8.47). A source S is placed
at the focal plane of 'the lens L and a parallel beam of light is incident on the front
85
M A M EL-Morsy
Optics II
Interference phenomena
surface at the plate A. It is _divided into two beams by the plate A. The beam 1
is reflected by the front surface and the beam 2 is reflected by the back
surface. The two beams are incident on the plate B and the beam 2 is reflected
by the front surface and the beam 1 is reflected by the back surface. The
emergent beams interfere and they are viewed by a telescope T which is focussed at
infinity.' Interference fringes are obtained. Here, the planes of A and B are
inclined at a small angle.
Fig. 8.47. Jamin's Refractometer
The tubes T1 and T 2 are evacuated and the fringes are observed in the field
of view of the telescope. The gas is allowed to enter one of the tubes and the
number of fringes that cross the centre of .the field of view is counted.
Suppose, n fringes have crossed the field of view. If the length of the tube is L,
the path difference introduced = ( µ - 1 ) L

1  L  n 
Therefore, the refractive index of the gas at a desired pressure can be
determined.
In order to avoid the counting of fringes every time, two compen sating
plates C 1 and C2 of equal thickness cut from the same piece, are
introduced in the beams 1 and 2 as shown in Fig. 8.47. The plates C1 and
C2 can be rotated about a common horizontal axis (at a fixed angle between them)
with the help of a calibrated circular disc, D.
When the disc D is rotated, the interfering beams passing through C and
C2 are affected such that in one case the path increases and in the other case it
decreases. The circular disc is calibrated by counting the number of fringes
directly and is marked in terms of the refractive index and the number of
86
M A M EL-Morsy
Optics II
Interference phenomena
wavelengths. Here, the tubes T 1 and T 2 are evacuated and using white light,
the telescope is focused such that the central white fringe is in the field of
view. The gas is introduced at a desired pressure an d temperature, into the
tube T 1 The central fringe shifts. With the help of the circular disc D, the
plate C 2 is rotated to bring the central fringe back to its original position.
The reading on the calibrated circular disc directly gives me refractive index or
me gas.
24- MACH-ZEHNDER REFRACTOMETER
It is used to study slight changes in refractive index of various gases
over a considerable region. Its principle is similar to Jamin's interferometer. The
mirrors M and M 2 work like the glass plate A and the mirrors M3 and M4
simalar to the glass plate B of a Jamin's refractometer. Moreover, the change
in the path difference takes place in the path of beam 1 (Fig. 8.48). The
number of fringes that cross the field of view o f the telescope can beobserved. Suppose the length of the tube T is L and n fringes cross the field
of view when the refractive index changes from µ1 to µ2 then
 2
 2
L  1 L   n 
 1
 
n 
L
87

L  n
M A M EL-Morsy
Optics II
Interference phenomena
Thus, the change in the refractive index can be calculated. This
refractometer is particularly useful in studying the flow pattern in wind
tunnels.
Example 60. In a Jamin's refractometer, two evacuated tubes each of length
20 cm are placed in the two beams. A gas at a known tem perature and pressure is slowly admitted in one of the tubes and
100 fringes cross the centre of the field of view. Calculate (i)
the refractive -index and (ii) the refractivity of the gas ( = 5460 A).
L  20 cm , n 100 ,   5460 x 10 8 cm

 1 L  n 
n 
100 x 5460 x 10 8
refractivity   1 

 2.73 x 10  4
L
20
n 
refractive index   1 
 1  2.73 x 10  4  3.73 x 10  4
L
Example 61. In a Mach- Zehnder refractometer, when one of the beams
passes through a wind tunnel of length 10 metres, 120 fringes
cross the centre of the field of view. Calculate the change in
refractive index.  = 5890 x 10-8 cm.
L  10 m  1000 cm, n  120,   5890 x 10 8 cm
 
n
120 x 5890 x 10 8

 7.068 x 10 6
L
1000
88
M A M EL-Morsy
Optics II
Interference phenomena
EXERCISES
1.
Light from an extended source fails obliquely on a thin film of an optical
medium. Find an expression for the effective path difference between a
part of a ray reflected externally at the first surface and the part which
suffers one reflection internally at the other face. Why does the film
appear black in reflected light when it is excessively thin '?
2.
How would you determine the wavelength of light with the Lloyd's mir ror
experiment ? In what respect do the fringes in this case differ from those
obtained with Fresnel's biprism.? How would you obtain achro matic
fringes with this arrangement ?
3.
Explain why different colours are exhibited by a thin film in white light.
When seen by reflected lig ht, why an excessively thin film appears to be
perfectly black ? With a suitable diagram, explain why a broad source of
light is needed to observe the phenomenon mentioned above.
4.
Give with necessary theory Newton's ring s method for the determination of
the wavelength of monochromatic tight. Why is the centre of the rings dark
and how can we. get a bright centre ?
5.
Explain Inc colours ;n thin films, How will you determine the wavelength of Light by Newton's rings ?
6.
How can Newton's rings be obtained in the laboratory ? How will you
use them to measure the waveleng th of sodium light ? Prove the necessary formula.
7.
Explain the colours of thin films. What are Newton's rings and how is
the wavelength determined using Newtons's rings ?
8.
State the conditions under. which light front two sources can i nterfere.
Describe the Fresnels biprism method of producing interference fringes
and determining the wavelength of light.
9.
Account for the colours in thin films. Explain how from a study of these
colours an estimate of the thickness of the film may be mad e. Prove any
formula you may need in this connection.
10.
What are coherent sources ? How are they realised in practice ? Describe a
method for determining the refractive index of a gas using the
interference phenomena.
89
M A M EL-Morsy
11.
Optics II
Interference phenomena
What is interference of light ? How will you determine the wavelength of
light using Fresnel's biprism ?
12.
Describe Michelson interferometer and show how it can be used for
measuring the wavelength of any line in a spectrum.
13. Describe Michelson interferometer How will you find the wavelength of
monochromatic light with its help 7 Derive the formula you use.
1 4 Explain the working of Michelson interferometer. How will you produce
circular fringes with it ? How will you measure the difference in wave length between the D lines of sodium light ?
15.
Explain with necessary theory the Newton's rings method of measuring the
wavelength of light.
16.
(Punjab)
Explain the principle of an interference refractometer. How would you
use it ID determine the refractive index of gas at different temperatures. ?
17.
Describe in detail how you would find-the wavelength of a monochromatic source using a Fresnel's biprism.(Mysore, Panjab, Agra)
18.
Explain clearly the theory and the experimental arrangement of Newton's rings experiment.
19.
. (Agra)
Describe the construction and working of Michelson interferometer. How
would you use it to measure the wavelength of a g iven line in the spectrum ? Under what conditions would you observe. the fringes in the
Michelson interferometer with white light '?
21.
Describe the construction of Michelson's interferometer and explain its
working. Discuss the important applications of the interferometer.
22.
Discuss the formation of colours in thin transparent film due to multiple
reflection of light in these and show that with monochromatic light the
interference patterns of the reflected and the transmitted light are complimentary.
23.
Explain how Newton's rings are formed and describe the method for the
determination of wavelength of light with their use.
24.
—
Give the theory of Newton's rings and describe a method of producing
them. Explain how this phenomenon can be used to determine the radius of
90
M A M EL-Morsy
Optics II
Interference phenomena
curvature of a plano-convex lens.
25.
26.
Describe and explain the phenomenon of interference in thin films .
What are Newton's rings and how are they formed ? How can the refractive index
of a liquid be determined using these fringes ? What is the difference between these
fringes and those produced by a biprism.
27.
Describe Michelson interferometer and explain the formation of fringes in
it. How was this interferometer used for the standardisation of the metre ?
52.
Describe the principle and working of a Michelson interferometer. How can
the instrument be used to determine the difference between the wavelength
of the Iwo D lines of sodium ?
53.
Explain how Newton's rings are formed and give a method for the determination of wavelength of light by Newton's rings method.
54.
What are coherent sources and how are they realised in practice ? How can
the wavelength of a monochromatic source of light be measured with the
help of a Fresnel's biprism ? Give the theory of the arrangement of the
apparatus.
55.
Describe Michelson's interferometer. Explain how circular, straight and
white light fringes are formed.
56.
Discuss the conditions for interference. Describe Young's experiment and
derive. an expression for (i) intensity at a point on the screen and (ii) fringe
width.
57.
Give the theory of Newton's rings and describe an experiment to de termine
of light using these rings.
58.
Explain with derivation of formula for tht. ff
C. 71
z
by
monochromatic light reflected normally. Account for perfect blackness of the
central spot. What is the difference between these fringes and those formed
by a biprism
59.
Describe the formation of fringes by Fabry-Perot interferometer and discuss
the intensity distribution.
60.
Explain the formation of Newtons's rings. How can these be used to
determine the refractive index of a liquid ?
91
M A M EL-Morsy
61.
Optics II
Interference phenomena
Show that the diameters of Newton's rings when two surfaces of radii R 1 and
R2 are placed in contact, are related by the equation.
62.
Explain the principle of Fabry-Perot etalon (or interferometer). Obtain an
expression for the intensity of the transmitted light through this etalon and
discuss the sharpness of fringes obtained.
63.
What is interference of light ? Describe Fresnel's biprism method for the
determination of wavelength of light.
64.
Describe the construction and working of Michelson interferometer
65.
What are coherent sources ? Explain the formation of colours in thin films.
Why are interference fringes not observed in thick films ?
Describe in detail an experiment to determine the wavelength of sodium light"
with Fresnel's biprism
67. Describe Michelson's interferometer. How will you use it to standardize
a metre in terms of wavelength of
68. What are coherent sources ? How can these be obtained ?
69. Give, with necessary theory, Newtons's rings method for the determi nation of the wavelength of monochromatic light. Why is the centre of
the rings dark and how can we get a bright centre ?
70. How can the wavelength of monochromatic light be measured with the
help of , a Freshet's biprism ? Give the theory and experimental
arrangement.
71. What is interference of light ? On its basis explain the colour effects
in thin films.
72. Write short notes on
(i)
Coherent sources.
(ii)
Fresnel's biprism.
(iii)
Lloyd's single mirror.
(iv)
Billet's split lens.
(v)
Achromatic fringes with white light.
(p it Cnlovc n f th ; r, niare.S.
(vii)
Testing the planeness of surfaces.
(viii)
Newton's rings.
(ix)
Haidinger fringes.
92
M A M EL-Morsy
Optics II
Interference phenomena
Brewster's fringes.
(x)
(xt) Non reflecting films.
(xii) Michelson interferometer and its uses
(.xiii) Standardisation of the metre.
(xiv)
Etalon.
(xv)
Jamin's refractometer
(xvi)
Mach-Zehnder refractometer.
(xvii)
Rayleigh's refractometer.
Fabry-Perot interferometer.
(xix) Lummer-Genrcke plate.
(x;c) Interference fringes.
Cu) Colour photography.
(xxii) Testing of Optical planeness
(xxii) Colours of thin films.
(xxiv) Interference filters.
73. A Fresnel biprism having angle of 1" and refractive index forms
interference fringes on a screen placed 80 cm from the prism. If the
distance between the source and the biprism is 20 cm, find the fringe separation
when the wavelength of light used is (a) 6900 A and (b) 4600 A
[Ans. (a) 1.975 x 10-2 cm (b) 1.317 x 10-2cm]
74. In Fresnel's biprism experiment, on inserting a thin plate of glass in the
path of the interfering beams, it is found that the central bright fringe shifts into
the position previously occupied by the sixth bright fringe.
If the wavelength of light used is 6 x 10-5 cm and the refractive index of the
glass plate is 1.5 for this wavelength, calculate the thickness of the plate.
[7.2 x 10-4cm]
75
- Newton's ring s are observed in reflected light of X = 5.9 x 10 -5cm. The
diameter of the 10 th dark ring is 0.50 cm. Find the radius of cur vature of
the lens and the thickness of the air film. [Ans. (i) 105.9cm (ii) 0.000295 cm]
_
76.
Interference fringes are produced with monochromatic light falling normally on a
wedge-shaped film of cellophane whose refractive index is 1.4. The angle of
93
M A M EL-Morsy
Optics II
Interference phenomena
the wedge is 40 seconds of an arc and the distance between the successive fringes
is 0.125 cm. Calculate the wavelength of light. Ans. 6.787 x 10-5 cm 2 p.
77.
In an experiment with a Michelson interferometer, the distance through which
the mirror is moved between two consecutive positions of maximum
distinctness is 0.2945 mm. If the mean wavelength for the two components
of the D lines of sodium light is 5893 A, deduce the difference between their
wavelengths.
78.
Describe Michelson's interferometer and explain the formation of cir cular
and straight fringes with it.
79.
Describe the construction and working a Fabry Perot interferometer.
80.
Explain why coherent sources are required for interference.
81.
What are coherent sources '? Give diagrams showing clearly how co herent sources are produced in (a) Newton's rings arrangement (b)
biprism arrangement.
82.
Describe an interference method for the measurement of radius of curvature
of a piano convex lens of power less than one diopter. Deduce the formula
used.
83.
Explain the formation of Fringes in a Fabry Perot interferometer and discuss the
effect of reflectivity on the sharpness of fringes.
84, What do you understand by coherent sources ? How are these obtained is
practice ? Why is it necessary to have coherent sources for observing
interference. of light
85.
With the help of a neat utagiani produce Newton's rims by reflected sodium
light. Prove that in reflected the diameter of the dark rings are
proportional to the square root of the natural numbers.
•
Why is it necessary to have a convex lens of large radius of curvature for
producing Newtons's rings
86.
Calculate the displacement of fringes when a thin transparent plate is
introduced is the path of . one of the interfering beams of monochromatic
light. How is this method used for finding the thickness of a thin mica sheet.
87.
Discuss die principle and' use of a Fabry Perot interferometer.
83. Explain Newton's rings method for determinin g the wavelength of
94
M A M EL-Morsy
Optics II
Interference phenomena
monochromatic light_ Why is the centre of the rings dark and how can
we get a bright centre ?
39. Describe Michelson's interferometer and discuss the conditions for
obtaining (1) circular fringes. (ii) straight line fringes with this interferometer.
91. Derive the expression for the resultant intensity when two coherent
beams of light are superposed.
What is the visibility of fringes :(a)
for two slits of equal intensities.
(b)
if intensity of one slit is 4 times the other ?
What will he the intensity when the two sources arc in-coherent ?
92. Explain what happens to Newton's rings when :(i) The lower glass plate is rough and not plane.
The lens is not in .contact with the_ glass plate.
Some oil is placed between the glass plate and the lens.
93. (a) Explain the working of Michelson's interferometer. How will you
produce circular fringes with it.
(h) Explain what is meant by the terms partial and temporal coherence ?
(c) Explain the term visibility of fringes. Obtain the expression for the
visibility of fringes in the case of Michelson's interferometer.
94. What are the various conditions for observing sustained interference.
Discuss, giving theory, the Newton's rings method for determinin g the
wavelength of a beam of monochromatic light.
95. (a) Obtain Airy's formula for the intensity of the transmitted light in
a Fabry Perot interferometer.
(b)
What do you mean by the term coefficient of finesse ?
(c)
Prove that the frin ges obtained with Fabry Perot interferometer are
sharper than those obtained with Michelson interferometer.
96.
(ci) Distinguish between spatial and temporal coherence.
(b) What are coherence length and coherence time ? Why is it impos sible to
observe interference between light waves emitted by independent sources ?
97.
Give a complete description of Michelson's interferometer. Discuss how the
95
M A M EL-Morsy
Optics II
Interference phenomena
wavelength of monochromatic radiation can be determined in the laboratory
with the help.of this interferometer.
98.
Discuss briefly the various methods for obtaining coherent sources of light
in the laboratory.
99. Show that the distance between the two virtual coherent sources in Fres nel's
biprisin arrangement is 2d(n 1)0 where d is the distance between the source
and the biprism, 0 is the angle of the biprism and n is the refractive index of
the material of the biprism.
96