M A M EL-Morsy Optics II Interference phenomena€¦ · Web viewM A M EL-Morsy Optics II Interference phenomena 89 89 17- NEWTONS'S RINGS When a piano-convex lens of long focal length

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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.

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Here, interference is due to reflected light. Therefore, for the bright rings

2 μ t cos θ = ( 2 n − 1 ) λ2

( i )

Where n = 1, 2, 3, …… etc.

Here is small, therefore cos = 1 and for air µ = 1

2 t = ( 2 n − 1 ) λ2

( ii)

For the dark fringe

2 μ t cos θ = n λ2 t = n λ

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 = tand

2 R − t = 2 R ( approximately )r2 = 2 R t

t = r2

2 RSubstituting the value of t in equations (ii) and (iii), For bright rings

r2 =(2 n − 1 ) λ R2

r = √ (2 n − 1 ) λ R2

For dark rings

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r2 = n λ Rr = √ n λ R

When n = 0, the radius of the dark ring is zero and the radius of

the bright rings is √ λ R2 . therefore, the center is dark.

Alternately dark and bright rings are produced ( Fig. 8.27).

Result . The radius of the dark ring is proportional to

(i) √ n

(ii) √ λ

and (iii) √ R .

Similarly the radius of the bright ring is proportional to

(i) √( 2 n −1 )

2

(ii) √ λ

and (iii) √ Rif D is the diameter of the dark ring

D = 2 r = 2 √ n λ RExample 8.46. A thin equiconvex lens of focal length 4 metres and

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reflective index 1.50 rests on and in contact with an optical

flat, and using light of wavelength 5460 A, Newton's rings

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

Dn = √ 2 (2 n −1 ) λ Rn = 5 , λ = 5460 x 10−8 cmf = 400 cm , μ = 1 .51f

= ( μ − 1 ) (1R1− 1

R2 )R1 = R , R2 = − R1f

= ( μ − 1 ) (2R )1400

= (1.5 − 1 ) (2R )R = 400 cmD = √ 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,

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calculate the wavelength of light used.

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 plano-

convex 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):

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For air

Dn+m2 = 4 ( n + m ) λ R

Dn2 = 4 n λ 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 μ t cos θ = n λ for dark rings

2 μ t = n λ

but t = r2

2 R2 μ r2

2 R= n λ

r2 = n λ Rμ

but r = D2

D2 =4 n λ Rμ

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

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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 surfaces. 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.

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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.

μ = ( D2

D1)2

= ( 1 .51 .35 )

2= 1 .235

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 stand ardization 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 M2 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

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S is equally reflected and transmitted by it. Light from a monochromatic

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 M1 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 M2. 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 M2 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 used between mirror M and A. The l ight

beam going towards 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.

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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 mir ror

M1 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- DETERMINATION OF THE WAVELENGTH OF

MONOCHROMATIC LIGHT

The mirrors M1 and M2 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 M 2 is kept fixed and

the mirror M1 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

field of view = n. Then, d = n λ

2 , because for one fringe shift, the mirror

moves through a distance equal to half the wavelength. Hence , can be

determined.

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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

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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 pres-

sures. 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

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the front 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 T2 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

( μ − 1 ) L = n λTherefore, 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 C1 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

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wavelengths. Here, the tubes T 1 and T2 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 and temperature, into the

tube T1 The central fringe shifts. With the help of the circular disc D, the

plate C2 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 M2 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 of the telescope can be-

observed. 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

( μ2 L − μ1 L ) = n λ

( μ2 − μ1 ) L = n λ

Δ μ = n λL

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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 , λ = 5460 x 10−8 cm( μ − 1 ) L = n λ

refractivity ( μ − 1 ) = n λL

= 100 x 5460 x 10−8

20= 2. 73 x 10−4

refractive index μ = 1 +n λL = 1 + 2 .73 x 10−4 = 3 .73 x 10−4

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 , λ = 5890 x 10−8 cm

Δ μ = n λL

= 120 x 5890 x 10−8

1000= 7 . 068 x 10−6

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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 light, 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 rings 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 wave-

length 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 wavelength of sodium light ? Prove the nec-

essary 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 interfere.

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 made. 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.

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11. 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. (Punjab)

16.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. . (Agra)

19.Describe the construction and working of Michelson interferometer. How

would you use it to measure the wavelength of a given line in the spec-

trum ? 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 com-

plimentary.

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

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curvature of a plano-convex lens.

25. Describe and explain the phenomenon of interference in thin films . 26. 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 de-

termination 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

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determine the refractive index of a liquid ?

61. Show that the diameters of Newton's rings when two surfaces of radii R1 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.

(pit Cnlovc n f th;r, niare.S.

(vii) Testing the planeness of surfaces.

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(viii) Newton's rings.

(ix) Haidinger fringes.

(x) Brewster's fringes.

(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 10-5cm 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 rings 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 curvature of

the lens and the thickness of the air film. [Ans. (i) 105.9cm (ii) 0.000295 cm]

_

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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

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 cur vature

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.

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87. Discuss die principle and' use of a Fabry Perot interferometer.

83. Explain Newton's rings method for determinin g the wavelength of

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 fringes 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 impossible to

96


observe interference between light waves emitted by independent sources ?

97. Give a complete description of Michelson's interferometer. Discuss how the

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 Fresnel'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.

M A M EL-Morsy Optics II Interference phenomena€¦ · Web viewM A M EL-Morsy Optics II Interference phenomena 89 89 17- NEWTONS'S RINGS When a piano-convex lens of long focal length

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