unit 1 optics jntu anantapur

engin

eerin

gphy

sics.w

eebly

.com

GLOBAL COLLEGE OF ENGINEERING &TECHNOLOGY: YSR DIST.

Unit –I OPTICS - Interference Engineering Physics

P.Sreenivasula Reddy M.Sc, (PhD) Website: www.engineeringphysics.weebly.com

P1

P2

1. Introduction In the 17th century, the properties of light were explained by Sir Isaac Newton

and Christian Huygens. Sir Isaac Newton was explained the properties of light by introducing corpuscular theory in 1675. It explains reflection, refraction and dispersion properties of light. It fails to explain interference, diffraction, polarization, photo electric effect and double refraction.

In 1679, Christian Huygens proposed the wave theory of light. According to Huygen’s wave theory, each point on the wave front is to be considered as a source of secondary wavelets. It explains reflection, refraction, dispersion, double refraction, diffraction, interference and polarization properties of light. It fails to explain, photo electric effect, black body radiation etc,. 2. Coherence

Coherence is a property of waves. Two produce interference pattern coherent sources are required. Coherent light sources cannot be obtained from the separate light sources, but they are obtained from the single light source.

Two waves are said to be coherent, the waves must have • Same wavelength • Same amplitude and • Constant phase difference

Definition:- A predictable correlation of the amplitude and phase at any one point with other point is called coherence. There are two types of coherence

i) Temporal coherence (or longitudinal coherence) ii) Spatial coherence (or transverse coherence)

Temporal coherence (or longitudinal coherence):- It is possible to predict the amplitude the amplitude and phase at a one point on the wave w.r.t another point on the same wave, then the wave is in temporal coherence. To understand this, let us consider two points 1P and 2P on the same wave as in shown in figure. Suppose the phase and amplitude at any one point is known, then we can easily calculate the amplitude and phase for any other point on the same wave by using the wave equation

� � � sin �2 ��

Where ‘a’ is the amplitude of the wave and ‘x’ is the displacement of the wave at any instant of time‘t’. Spatial coherence (or transverse coherence)

It is possible to predict the amplitude the amplitude and phase at a one point on the wave w.r.t another point on the second wave, then the wave is in spatial coherence.

engin

eerin

gphy

sics.w

eebly

.com

Independent sources are not coherent Two independent sources of light with same power can never be treated as coherent sources; even it emits same wavelength and same amplitude waves. Generally the light is emitted from the source through spontaneous emission process. But the waves emitted trough spontaneous emission process is in out of phase. So two waves generated by two light sources are always in out of coherence. Even the waves are emitted from the different parts of the lamp, no longer they are coherent. 3. Principle of superposition of waves

Definition:-

Principle of superposition of waves states that, the resultant displacement of two or more waves traveling simultaneously in a medium at any point is equal to the algebraic sum of the displacements due to individual waves.

To understand this concept, Let us consider two waves traveling simultaneously in the

medium. Let �� and �� are the displacements of first and second waves at any point in the absence of other.

According to principle of superposition, the resultant displacement �� of two waves can be written as � � ��

Let two waves are in phase, their resultant amplitude is � � ��

Two waves are in opposite phase, their resultant amplitude is � � ��~ ��

4. Young’s double slit experiment

The first experimental evidence of interference pattern was given by Thomas Young In 1801. He explained the interference pattern based on the wave nature of light. Experimental setup:

His experimental arrangement is shown in figure. He passed the sun light through a narrow pin hole S on a opaque surface and then through closely spaced pin holes S1 and S2 in another opaque surface. A screen XY was arranged in front of the pin holes S1 and S2. He observed few coloured bright and dark bands on the screen. Now a day, the pin holes are replaced by slits and sun light is replaced by monochromatic light.

S

S1

S2 Screen

Y

X

+

Wave 1

Wave 2 =

+

Wave 1

Wave 2 =

engin

eerin

gphy

sics.w

eebly

.com




Explanation of wave theory

When sun light is passes through pin hole S, spherical waves are spread out. According to Huygen’s wave theory, each point on the wave front is to be considered as a source of secondary wavelets. Hence spherical waves also spread out from pin holes S1 and S2. The radii of the wave fronts increase as they move away from S1 and S2 and hence superimpose on each other. In the above figure, continuous circular arcs represent the wave crests while dotted circular arcs represent the troughs of each wave. A crest fall on the other crest constructive interference will occurs and their resultant amplitude is equal to the sum of the amplitudes individual waves. � � ��

A crest fall on the other trough destructive interference will occurs and their resultant amplitude is equal to the difference of the amplitudes of individual waves. � � �� Thus a number of dark and bright bands having equal width is observed on the screen. 5. Interference of light

The best evidence for the wave nature of light is interference phenomenon. This was experimentally demonstrated by Thomas Young in 180, through double slit experiment. Due to interference, we will observe many observations in our day today life, such as multiple colours on soap bubbles as well as on oil film when viewed under sun light. Interference concept is explained on the basis of superposition of wave’s concept.

When two light waves superimpose, then the resultant amplitude or intensity in the region of superposition is different than the amplitude of individual waves.

Definition:- The modification in the distribution of intensity in the region of superposition is known

as interference. In case of interference pattern we observe two cases

• Constructive interference

• Destructive interference

Constructive interference � The waves are reaching at a point are in phase constructive interference occurs � In constructive interference, the resultant amplitude is always equal to the sum of the

amplitudes of two individual waves.

� Condition

The path difference between the two waves is equal to the integral multiple of wave

length �� the constructive interference occurs. �� Where n = 0, 1, 2, 3, 4 …

+

Wave 1

Wave 2 =

engin

eerin

gphy

sics.w

eebly

.com

Destructive interference � The waves are reaching at a point are in out of phase desstructive interference occurs � In Destructive interference, the resultant amplitude is always equal to the difference of the

amplitudes of two individual waves. � Condition

The path difference between the two waves is equal to the odd integral multiple of λ/2 destructive interference occurs

�� 2 � 1�2 Where n � 1, 2, 3, 4 … *�

�� +,��-� Where n � 0, 1, 2, 3, 4 …

6. Types of interference:-

For the formation of interference pattern, two coherent light sources are required. To get two coherent sources form a single light source, two techniques are used. They are

1. Division of wave front 2. Division of amplitude

Division of wave front The wave front from a single light source is divided into two parts using the phenomenon of reflection, refraction or diffraction. Young’s double slit experiment is belongs to this class of interference.

Division of amplitude The amplitude of a single light beam is divided into two parts by parallel reflection or refraction. Newton’s ring experiment, Michelson’s interferometer is belongs to this class of interference. 7. Conditions for interference

1) Two light sources of emitting light waves should be coherent. 2) Two sources must emit continuous light waves of same wavelengths or frequency. 3) The separation between the two sources should be small. 4) The distance between the two sources and the screen should be large. 5) To view interference fringes, the background should be dark. 6) The amplitude of light waves should be equal or nearly equal. 7) The sources should be narrow. 8) The sources should be monochromatic.

8. Interference in thin films by reflection

Principle:- The formation of colours in thin films can explained as due to the phenomenon of

interference. In this example, the formation of interference pattern is by the division of amplitude. . Consider a thin film of uniform thickness ’�’ and refractive index ‘µ’. Let a monochromatic light ray AB is incident is on the upper surface of the film with an angle ‘i’. This ray is partially reflected along BC and the remaining part is refracted along BD with an angle ‘r’. The refracted ray BD is reflected into DE from the lower surface of the film and it emerges through the film in the form of light ray EF. The two light rays BC and EF are parallel and superimpose and produce interference. The intensity of interference fringe depends up on the path difference between the ray 1 and ray 2.

+

Wave 1

Wave 2 =

engin

eerin

gphy

sics.w

eebly

.com




To find out the path difference between the light rays (1) and (2), draw one

normal DG to BE and from point E to BC. From point E and H onwards the two light

rays 1 and 2 travels equal distances. By the time the light ray 1 travels from B to H, the

transmitted ray has to travel from B to C and D to E.

The path difference between the light rays (1) and (2) is

�� 0�12 � 23� � ��45 � 16 � �� (1)

From ∆128 cos � � ;<=; � >

=;

12 � �cos �

Similarly from ∆238 cos � � ;<;? � >

;?

23 � �cos �

@ 12 � 23 � >ABC D (2)

From ∆136 sin � � =E=? � =E

=<,<?

@ 16 � �18 � 83�. sin � From ∆128 � � ∆238 18 � 83 � � tan �

16 � �2� tan ��. sin � From Snell’s law at point B

sin � � 0 sin �

@ 16 � 20� tan � . sin � (3)

Substituting the equations (2) and (3) in equation (1), we get

I�� J>KLM D � 20� tan � . sin �

Ray 1

Ray 2

engin

eerin

gphy

sics.w

eebly

.com

� 20�cos � � 20�. sin � �

cos �

� 20�cos � �1 � sin � ��

� 20�cos � �*N ��

=20� cos �

At point B the light ray (1) is reflected at the surface of thin film (denser medium). So the light ray (1) undergoes a phase change π or an additional path difference λ/2.

Total path difference � 20� cos � � -�

Constructive interference (or Bright fridge) General condition; ��

20� cos � � 2 �

20� cos � � � 2

20� cos � � �2 � 1�2

Destructive interference (or Dark fridge) General condition: �� 2 � 1� -

�

20� cos � � 2 � �2 � 1�

2

20� cos � �

9. Newton’s rings

Principle:-

The formation of Newton’s rings can explained as due to the phenomenon of interference. In this example, the formation of interference pattern is obtained by the division of amplitude. Experimental arrangement The experimental arrangement of Newton’s rings is shown in figure. The Plano -convex lens (L) of large radius of curvature is placed with its convex surface on the glass plate (P). The lens touches the glass plate at O. A monochromatic light is allowed to fall normally on the lens with the help of glass plate M kept at 450 to the incident monochromatic light.

A part of light is reflected by

the curved surface of the lens ‘L’ and a part of light is transmitted is partly reflected back by the upper surface of the plane glass plate P as shown in figure. These reflected rays interfere and give rise to an interference pattern in the form of circular fringes. These rings are seen through microscope.

M

O

engin

eerin

gphy

sics.w

eebly

.com




Explanation of formation of Newton’s rings

Newton’s rings are formed due to the interference between the light rays reflected from the lower surface of the lens and the upper surface of the glass plate (or top and bottom surfaces of the air film).

Let R be the radius of curvature of the lens and � be the thickness of the air film at point P. At point P a part of the incident monochromatic light is reflected from the bottom surface of the glass plate without phase change. The other part of the light is refracted from the upper surface of glass plate with additional phase change of π or path difference λ/2. The path difference between the two rays is

20� cos � � 2

For air film 0 � 1 and for normal incidence � � 0, so

The path difference � 2� � -�

Constructive interference (or Bright fridge) General condition: ��

2� � 2 �

2� � �2 � 1� 2

Where � 0, 1, 2, … … … .. Destructive interference (or Dark fridge) General condition: �� 2 � 1� -

�

2� � 2 � �2 � 1�

2

2� �

Where � 0, 1, 2, … … … .. At the point of contact � � 0, path difference is

-� i.e., the reflected and incidence light are out

of phase and destructive interference occur. So the center fringe is always dark. Theory of Newton’s rings

To find the diameters of a dark and bright fringes construct a circle with the radius of curvature R of a lens L and let us choose a point P at a distance ‘r’ from the center of lens and � be the thickness of air film at point I. From the property of a circle OI. O1 � OP. O2

�. � � Q. �2� � �� 2R� � ��

If t is small �� is negligible. �� 2R�

� � ��2R

Bright rings

For bright ring, the condition is 2� � �2 � 1� -�

2 ��2R � �2 � 1�

2

�� 2 � 1�R2

r r

engin

eerin

gphy

sics.w

eebly

.com

By replacing r by D/2 the diameter of the bright ring is

2�4 � �2 � 1�R

2

2� � 2�2 � 1�R

2 � S2�2 � 1�R

2 � S�2 � 1�√2R

2 U S�2 � 1�

2 U √*�� V��4 V5W��

Dark rings

For dark rings, the condition is

2� �

2 ��2R �

�� R

By replacing r by D/2 the diameter of the nth dark ring is

2�4 � R

2 � √4 R

2 � 2√ R

2 U √

2 U √ ��V��4 V5W��

Note: suppose a liquid is taken in between the lens and glass plate having refractive index 0,

then the diameter of the dark nth dark ring can be written as

2 � √4 R0

10. Determination of wave length of sodium light u sing Newton’s rings

By forming Newton’s rings and measuring the radii of the rings formed, we can calculate the wavelength of the light used if the radius of curvature of the lens is known. Let R be the radius of curvature of the lens and is the wavelength of the light used. So the diameter of the nth dark ring can be written as 2+� � 4 R (1)

Similarly the diameter of the (n+m)th dark ring is

2+,X� � 4 � � 5� R (2)

Subtracting equation (1) from (2) we get

2+,X� � 2+� � 4 � � 5� R � 4 R

2+,X� � 2+� � 4 5 R

� 2+,X� � 2+�45R

Using the above relation wavelength can be calculated

engin

eerin

gphy

sics.w

eebly

.com




11. Determination of refractive index of a liquid u sing Newton’s rings

By forming Newton’s rings and measuring the diameter of the rings formed, we can

calculate the refractive index of the liquid.

In air film, the diameter of the nth and mth dark rings are 2+ and 2X are measured

with the help of travelling microscope.

The diameter of the nth dark ring is

2+� � 4 R (1)

The diameter of the mth dark ring is

2X� � 4 5 R (2)

So 2X� � 2+� � 4 5 R � 4 R

2X� � 2+� � 4 �5 � � R (3)

The Newton’s rings setup is taken in a liquid. Now the air film is replaced by liquid film. In liquid film, the diameters of the same nth and mth dark rings are 2′+ and 2′X are measured with the help of travelling microscope.

2′+� � Y + - ZJ and

2′X� � 4 5 R0

So 2′X� � 2′+� � Y �X[+� - ZJ (4)

Dividing equation (3) by (4)

2X� � 2+�2′X� � 2′+� � 4 �5 � � R

4 �5 � � R0

2X� � 2+�2′X� � 2′+� � 0

Using the above relation 0 can be calculated.

engin

eerin

gphy

sics.w

eebly

.com

engin

eerin

gphy

sics.w

eebly

.com

GLOBAL COLLEGE OF ENGINEERING &TECHNOLOGY: YSR DIST. Unit –I OPTICS - Diffraction Engineering Physics

P.Sreenivasula Reddy M.Sc, (PhD) Website: www.engineeringphysics.weebly.com Page 1

Introduction

The wave nature of light is first confirmed by the phenomenon of interference. Further it is confirmed by the phenomenon of diffraction. The word ‘diffraction’ is derived from the Latin word diffractus which means break to piece. When the light waves encounter an obstacle, they bend round the edges of the obstacle. The bending is predominant when the size of the obstacle is comparable with the wavelength of light. The bending of light waves around the edges of an obstacle is diffraction. It was first observed by Gremaldy.

1. Diffraction

Definition:-

When the light falls on the obstacle whose size is comparable with the wavelength of light then the light bends around the obstacle and enters in the geometrical shadow. This bending of light is called diffraction.

When the light is incident on an obstacle AB, their corresponding shadow is completely dark on the screen. Suppose the width of the slit is comparable to the wavelength of light, then the shadow consists of bright and dark fringes. These fringes are formed due to the superposition of bended waves around the corners of an obstacle. The amount of bending always depends on the size of the obstacle and wavelength of light used. 2. Types of diffraction

The diffraction phenomena are classified into two ways I. Fresnel diffraction

II. Fraunhofer diffraction.

Fresnel diffraction:-

In this diffraction the source and screen are separated at finite distance. To study this diffraction lenses are not used because the source and screen separated at finite distance. This diffraction can be studied in the direction of propagation of light. In this diffraction the incidence wave front must be spherical of cylindrical.

Fraunhofer diffraction:-

In this diffraction the source and screen are separated at infinite distance. To study this diffraction lenses are used because the source and screen separated at infinite distance. This diffraction can be studied in any direction. In this diffraction the incidence wave front must be plane.

engin

eerin

gphy

sics.w

eebly

.com

3. Fraunhofer single slit diffraction:-

Let us consider a slit AB of width ‘e’. Let a plane wavefront of monochromatic light of wavelength λ is incident on the slit AB. According to Huygens principle, every point on the wavefront is a source of secondary wavelets. Those secondary wavelets travelling normal to the slit are brought to focus at point P0 on the screen by using the lens. The secondary wavelets traveling at an angle θ with the normal are focused at point P1.

Intensity at point P1 depends up on the path difference between the wavelets A and B reaching to point P1.

2

2 sin

Let the width of the slit is divided into ‘n’ equal parts and the amplitude of the wave front each part is ‘a’. Then the phase difference between any two successive waves from these parts would be

1

1 2 sin

Using the vector addition method, the resultant amplitude R is sin 2sin 2

sin. 1 2 sin

2

sin1 2 sin

2

sin sin

sin sin

sin

sin

sin

sin sin

sin

sin

Therefore resultant intensity

engin

eerin

gphy

sics.w

eebly

.com



Principal maximum:- The resultant amplitude R can be written as

3! 5! 7!

1 3! 5! 7!

1 3! 5! 7!

In the above expression for 0 values the resultant amplitude is maximum Then

sin0

sin 0 0

For 0 value the resultant intensity is maximum at P0 and is known as principal maximum. Minimum intensity positions Will be minimum when sin 0

1,2,3,4,5 … … .. sin

sin So we obtain the minimum intensity positions on either side of the principal maxima for all

values. Secondary maximum

In between these minima secondary maxima positions are located. This can be obtained by differentiating the expression of w.r.t and equation to zero

sin0

2sin sin0

2sin·

cos sin0

In the above expression can never equal to zero, so Either sin 0 or cos sin 0 sin 0 gives the positions of minima. The condition for getting the secondary maxima is

cos sin 0 cos sin

tan The values of satisfying the above equation are obtained graphically by plotting the curves and tan on the same graph. The plots of

and tan is shown

in figure.

engin

eerin

gphy

sics.w

eebly

.com

From the graph intersecting points are 0, , , ………… From the above concepts the intensity distribution curve verses is shown in figure.

4. Fraunhofer double slit diffraction Let S1and S2 be the two slits equal width e and separated by a distance d. The distance between the two slits is (e + d). A monochromatic light of wavelength λ is incident on the two slits. The diffracted light from these slits is focused on the screen by using a lens. The diffraction of a two slits is a combination of diffraction and interference. The wavelets travelling normal to the slit is focused at P0. The wavelets travelling at an angle θ with the incident light are focused at point P1.

From Fraunhofer single slit experiment, the resultant amplitude is So the amplitude of each secondary wavelet travelling with an angle θ can be taken as sin . These two wavelets interference and meet at point P1 on the screen.

engin

eerin

gphy

sics.w

eebly

.com



To find out the path difference between the two wavelets, let us draw a normal s1k to the wavelet S2.

S From ∆S S k sin S

S SS

S sin

2

2

sin

By using vector addition method, we can calculate the resultant amplitude at point P1 2 cos

sin sin2

sin sincos

2sin

2sin

cos

2sin

1 cos

2sin

1 2 cos 1

2sin

2 cos

4sin

cos

4sin

cos

sin

4sin

cos

The resultant intensity 4 cos From the above equation, it is clear that the resultant intensity is a product of two factors i.e.,

1. represents the diffraction pattern due to a single slit.

2. cos represents the interference pattern due to wavelets from double slit. Diffraction effect In diffraction pattern the variation of w.r.t as shown in figure.

engin

eerin

gphy

sics.w

eebly

.com

The diffraction pattern consists of central principal maxima for 0 value. The secondary maxima of decreasing intensity are present on either side of the central

maxima for , , values.

Between the secondary maxima the minima values are present for , 2 , values. Interference effect In interference pattern the variation of cos w.r.t as shown in figure. cos represents the interference pattern. Interference maximum will occur for cos 1

0, 1, 2, 3, 4 … … … , 2 , 3 , 4 … … …

sin

sin Interference minima will occur for cos 0

2 1 2

sin2 1

2

sin 2 1 2 The resultant intensity variation due both interference and diffraction patterns is shown in figure. Due to interference the resultant minimum in not exactly equal to zero.

engin

eerin

gphy

sics.w

eebly

.com



Construction of plane diffraction grating

Or Construction of grating

A set of large number of parallel slits of same width and separated by opaque spaces

is known as diffraction grating. Fraunhofer used the first grating consisting of a large

number of parallel wires placed side by side very closely at regular separation. Now the

gratings are constructed by ruling the equidistance parallel lines on a transparent material

such as glass with fine diamond point. The ruled lines are opaque to light while the space

between the two lines is transparent to light and act as a slit.

Let ‘e’ be the width of line and‘d’ be the width of the slit. Then (e + d) is known as

grating element. If N is the number of lines per inch on the grating then

1 2.54 .

Plane Diffraction grating ( or diffraction at N - slits)

Let a plane wavefront of monochromatic light of wavelength λ is incident on the

slits. Let ‘e’ be the width of line and ‘ ’ be the width of the slit. Then (e + d) is known as

grating element. According to Huygens principle, every point on the wavefront is a source

of secondary wavelets. The wavelets spread out to the right in all directions. Those

secondary wavelets travelling normal to the slit are brought to focus at point P0 on the

screen by using the lens. . The wavelets travelling at an angle θ with the incident light are

focused at point P1.

θ

engin

eerin

gphy

sics.w

eebly

.com

The resultant amplitude due to diffraction of a single slit is sin , where

sin . Let us assume that there are N slits in the grating. The path difference between the

corresponding points is

sin 2 .

The resultant of amplitude R of the N amplitudes of is

sin sinsin

1

And intensity is sin

.sinsin

2

In the above equation shows the intensity distribution due to a single slit

diffraction and shows the combined intensity distribution due to interference at all

the N slits. Principal Maxima: from equation 2, we know that the intensity would be maximum when sin 0, where 0, 2 , … . . and n= 0,1,2,3…

Indeterminate

To find out its value, L- Hospitals rule is applied

lim sin

sin lim

sin

sinlim

coscos

Hence the resultant intensity is can be written as sin

So the maxima are obtained for sin or

sin Minima: From equation 2 the resultant intensity is minimum for sin 0 but sin 0

sin

sin can be take integral values except 0, N, 2N,………..nN. For these values we bet maxima

Secondary maxima: Between two adjacent principal maxima there are 1 minima and 2 other maxima called secondary maxima.b to get the position so secondary maxima, differentiate equation 2 w.r.t and then equate to zero.

engin

eerin

gphy

sics.w

eebly

.com



sin 2

sinsin . cos sin sin cos

2 0

cos sin sin cos 0 or tan tan

The roots of the above equation (other than , this corresponds to principal maxima) give the secondary maxima.

The variation of intensity due to the interference factor is shown in figure

The variation of intensity due to the diffraction factor of is shown in figure

The variation of resultant intensity is shown in figure.

engin

eerin

gphy

sics.w

eebly

.com

5. Grating spectrum When white light is fall on the grating, the light gets diffracted through each slit. As a

result of both interference and diffraction, diffraction pattern will occur. This pattern is known as grating spectrum or diffraction spectrum.

The condition for the principal maximum in grating spectrum is sin

Where is the grating element and is the order of spectrum. From the grating equation, we observe that

1. For a particular wavelength λ the angle of diffraction θ is different for principal maxima and for different orders.

2. For white light and for a particular order , the light of different wavelengths will be diffracted in different directions.

3. Angle of diffraction increases with wavelength. 4. In the spectrum violet is in the innermost position and red at the outermost position. 5. Most of the energy is distributed for zero order and the rest is distributed among the

other orders. 6. Spectrum different orders are situated symmetrically on both sides of zero order. 7. Sharpness of maxima increases with increasing of number of lines in the grating. 8. The colour of central maxima is same as the incident light. 9. The condition for finding the maximum number of orders formed by the grating is

engin

eerin

gphy

sics.w

eebly

.com

GLOBAL COLLEGE OF ENGINEERING &TECHNOLOGY: YSR DIST. Unit –I OPTICS - polarisation Engineering Physics

P.Sreenivasula Reddy M.Sc, (PhD) Page 1 of 9

Introduction

From the previous chapter’s interference and diffraction, we can understand that the light is exhibiting wave nature. But these phenomenon don’t explain the character of these wave motion i.e., whether it is longitudinal or transverse. In longitudinal waves, the particles of the medium move to and fro in the direction of propagation of the wave as in case of sound waves. In transverse waves, the particles of the medium vibrate up and down perpendicular to the direction of propagation of wave as ripples on a water surface.

1. Polarization

Light is electromagnetic in nature, it consists of oscillating electric and magnetic fields of vectors. They are perpendicular to each other and perpendicular to the propagation of light.

In light, the electric field direction is always changes in random ways. So the unpolarized or ordinary light is represented as shown in figure.

If the direction of electric field vector is confined to one fixed direction, that light beam is

called linearly polarized or plane polarized light. So the plane polarized light is represented as shown in figure

Definition:

The process of restricting the vibration of electric field vector is called polarization.

2. Plane of polarization and plane of vibration

Plane of vibration: - The plane which contains the vibrations of polarized is known as plan of vibration.

Plane of vibration:- The plane perpendicular to the plane of vibration is known as plane of polarization. When an unpolarized light is incident on the polarizer, the emergent light beam always has

vibrations parallel to the optic axis. In the figure the plane parallel to the optic axis of the polarizer and containing the

vibrations of polarized light and hence it is known as plane of vibration the plane is perpendicular to the plane of vibration and hence it is known as plane of polarization.

engin

eerin

gphy

sics.w

eebly

.com

3. Definitions: Blunt corners:- If any corner contain all obtuse angles (is an angle between 90 and 180 degrees), which is called blunt corner.

Optic axis: - A line joining the two blunt corners is known as optic axis of the crystal. An optic axis is not

an axis, but it is a direction of a crystal. Any line parallel to the optic is also known as optic axis.

Uniaxial crystal: - If any crystal having only one optic axis is known as uniaxial crystal. Examples: - calcite, quartz.

Biaxial crystal: - If any crystal having two optic axes is known as biaxial crystal. Examples: -borax, mica.

Principal section: - A plane containing the optic axis and perpendicular to two opposite faces of the crystal is

known as the principal section of the crystal.

Principal planes: - The plane having the optic axis and ordinary ray of the crystal is known as principal plane of

the ordinary ray. The plane having the optic axis and extraordinary ray of the crystal is known as principal plane of the extraordinary ray.

4. Production of polarized light For the production of plane polarized light different methods are followed, they are

a) Polarization by reflection b) Polarization by transmission c) Polarization by absorption d) Polarization by double refraction

a) Polarization by reflection

When the unpolarized light is fall on the smooth surface such as glass or water surface, the reflected light is partially plane polarized. The degree of polarization changes with the angle of incidence. For a particular angle of incidence the reflected light was completely polarized transmitted light ray is partially plane polarized. The vibration of the reflected light is perpendicular to the plane of incidence. The polarizing angle for glass is 57.50 At which angle of incidence the reflected ray is completely plane polarized, that angle is called polarizing angle or angle of polarization.

engin

eerin

gphy

sics.w

eebly

.com



b) Polarization by transmission

When the unpolarized light incident on smooth surface at polarizing angle the reflected light is plane polarized and the transmitted light ray is partially plane polarized.

When the unpolarized light incident on the pile of plates at polarizing angle, the transmitted light ray is purely plane polarized. The polarizing angle for glass is 57.50. The vibration of the transmitted light is parallel to the plane of incidence.

c) Polarization by absorption When un polarized light is passing through the tourmaline ( , , , it is split into

horizontal and vertical components. The horizontal components are completely absorbed by the crystal and the vertical component comes out. The light coming from the crystal is linearly polarized.

d) Double refraction: -

When an unpolarized light is passes through a calcite crystal, it is split up into two plane polarized lights. This phenomenon is known as double refraction.

In which, one ray obeys the laws of refraction and has vibrations perpendicular to the principal

section is known as ordinary ray. The other ray does not obey the laws of refraction and has vibrations parallel to the principal section is known as extraordinary ray. The refractive index of ordinary and extraordinary rays for calcite crystal is

sinsin

sinsin

In calcite crystal the velocity light for O- ray inside the crystal is less than the E- ray. The refractive index of O-ray is same for all angle of incidence and hence it is represented by spherical wave front. The refractive index of E-ray is always varies with the angle of incidence and hence it is represented by ellipsoidal wave front. But both rays are travel with same velocity along the optic axis of the calcite crystal.

engin

eerin

gphy

sics.w

eebly

.com

5. Polarization of light waves Let us consider an unpolarized light is passed through the tourmaline crystal as shown in

figure. Even when we are rotating the tourmaline crystal by taking the incident ray as an axis, there is no intensity variation in the emergent beam. The tourmaline crystal only allows the vibrations of light that are parallel to the axis of the crystal, and it does not allow the other vibrations. So the emergent beam from the tourmaline crystal is a polarized light. So the first tourmaline crystal is called polarizer.

If the second tourmaline crystal is rotated by taking the incident ray as an axis, the intensity of emergent beam from the second tourmaline crystal has two times minimum intensity and two times maximum intensity is observed within one complete rotation. When the second tourmaline crystal is parallel to the first one the emergent beam from the second crystal is maximum. When the second tourmaline crystal is perpendicular to the first one the emergent beam from the second crystal is minimum. Therefore the second crystal is called analyzer. So this property of light of rays confirms the transverse nature of light rays. 6. Nicol prism

Nicol prism is an optical device made from calcite and is used to produce and analyze plane polarized light. It was invented by Nicol in 1828 and is known as Nicol prism. Principle:-

Nicol prism is worked on the principle of double refraction exhibited by calcite crystal. Construction:-

Nicol prism is constructed by using calcite crystal. Its length and breadth dimensions are in the ratio 3:1. Consider a calcite crystal, in which is the principal section and B and D are blunt corners. The angles of the principal section are 710 and 1090. The angle of the principal section is reduced from 710 to 680 by grinding the faces of AB and CD. After grinding the new principal section is

The crystal is cut into two pieces perpendicular to the principal section along . The two cut surfaces are highly polished into optical flat and joined together by means of Canada balsam. The refractive index of Nicol prism for sodium wave length 5893 and the refractive indices of ordinary ray, extraordinary ray and Canada balsam are 1.658, 1.46 and 1.55 respectively. The two faces of the Nicol prism is kept open, while the two sides are blackened to absorb the totally internally reflected rays.

C

D

B

A

Canada balsam cement

68 71

engin

eerin

gphy

sics.w

eebly

.com



Working of Nicol prism When an unpolarized light is passes through a calcite crystal, it is split up into two beams, namely, ordinary and extraordinary rays.

When the ordinary ray passing through the calcite, the Canada balsam layer acts as a rarer medium. Therefore the ordinary ray is travelling from denser (calcite) to rarer (Canada balsam) medium. For ordinary ray, the angle of incidence at the interface of calcite and Canada balsam is greater than the critical angle, it undergoes total internal reflection. The critical angle for the ordinary ray is

sin1.551.658 69.2

The angle of the principal section is greater than the critical angle, so the upper and lower surfaces of the Nicol prism are grounded from 710 to 680. For the extraordinary ray the Canada balsam is acts as a dense medium. Hence it travels in a straight line and emerges out from the Nicol prism. The emergent beam is plane polarized light.

7. Plane polarized light by Nicol prism. A Nicol prism is used to produce and analyze plane polarized light. When an unpolarized

light is passed through a Nicol prism, it is split up into ordinary and extraordinary rays. The ordinary ray is cut of when it is passing from calcite to Canada balsam layer. The extraordinary ray is passed through the Nicol prism.

If the second Nicol prism is rotated by taking the incident ray as an axis, the intensity of emergent beam from the second Nicol prism has two times minimum intensity and two times maximum intensity is observed within one complete rotation. The first Nicol prism is known as polarizer and the second Nicol prism is known as analyzer. Thus a Nicol prism can be used as a polarizer as well as analyzer.

E ray

engin

eerin

gphy

sics.w

eebly

.com

8. Limitations of Nicol prism 1. The Nicol prism acts as a polarizer only for the light rays having slightly convergent and slightly

divergent beam. 2. The Nicol prism does not acts as a polarizer for the light rays having highly convergent and highly

divergent beam 3. If the incident divergent beam is making larger angle with the front face, the extraordinary ray

will become parallel to the optics axis of the crystal. Extraordinary ray also totally internally reflected by the Canada balsam layer. Therefore no light emerges our from the Nicol prism.

4. If the incident convergent beam is making small angle with the front face, the ordinary makes less critical angle at the calcite and Canada balsam interface. Then the ordinary ray also emerges out from the Nicol prism.

9. Quarter wave plate

A wave plate is an optical device, is used to produce path difference or phase difference between the ordinary and extraordinary rays. It is made from the doubly refracting uniaxial crystals. Its faces are cut parallel to the direction of the optic axis.

When the polarized light is incident on the calcite crystal, the light splits up into O-ray and E-ray. The thickness of the device is cut in such way it can produce the path difference 4 or phase difference 2 between the O-ray and E-ray is called quarter wave plate.

Let be the thickness of the crystal. Let and be the refractive indices of E-ray and O-ray. Then the path difference between E-ray and O-ray is

For quarter wave plate path difference = 4

4

4

For negative crystals

For positive crystals

10. Half wav e plate A wave plate is an optical device, is used to produce path difference or phase difference

between the ordinary and extraordinary rays. It is made from the doubly refracting uniaxial crystals. Its faces are cut parallel to the direction of the optic axis. When the plane polarized light is incident on the calcite crystal, the light splits up into O-ray and E-ray. When the refracting faces are cut parallel to the optic axis, O-ray and E-ray travels with different velocities along the same path. The thickness of the device is cut in such way it can produce the path difference 2 or path difference between the O-ray and E-ray is called half wave plate. Let be the thickness of the crystal. Let and be the refractive indices of E-ray and O-ray. Then the path difference between E-ray and O-ray is

For half wave plate path difference = 2

2

2

For negative crystals

For positive crystals

engin

eerin

gphy

sics.w

eebly

.com



11. Theory of circular and elliptical polarized lights A beam of plane polarized light is obtained by passing the unpolarized light through the Nicol

prism. Let be the maximum amplitude of the incident light which makes an angle with the optic axis. When the plane polarized light is passes through a wave plate, it is split up into two ordinary and extraordinary rays. The amplitudes of ordinary and extraordinary rays are sin and cos respectively.

The ordinary and extraordinary rays travel with different velocities in the same direction, and

hence a phase difference is introduced between these two rays. Let be the phase difference between

the ordinary and extraordinary rays. The emergent beam from the wave plate can be represented as

cos sin (1)

sin sin (2)

Taking cos and sin , the above equations can be written as

sin (3)

sin (4)

Equations (3) and (4) can be written as

sin (5)

sin (6)

Equation (5) can be written as

sin cos cos sin (7)

Substituting the value of sin and cos from equation (6) in equation (7)

cos 1 sin (8)

Squaring equation (8), we get

cos 2 cos 1 sin

cos 2 cos sin sin

cos sin 2 cos sin

2 cos sin (9)

P

Q A sin

A cos

engin

eerin

gphy

sics.w

eebly

.com

Equation (9) is a general expression for an ellipse. when 0, sin 0 and cos 1

Equation (9) becomes

2 0

0

The above expression represents a straight line. Therefore the light is plane polarized. when , sin 1 and cos 0

Equation (9) becomes

1

This represents the equation of a ellipse. Thus the emergent light in this case will be elliptically polarized light.

when , sin 1, cos 0 and

1

This represents the equation of a circle. Thus the emergent light in this case will be circularly polarized light

12. Differences between polarized light and unpolarized light

Unpolarized light Polarized light When an unpolarized light is passed through the rotating tourmaline crystal, no variation intensity of light is observed.

When a polarized light is passed through the rotating tourmaline crystal, variation in the intensity of light is observed.

The unpolarized light is symmetrical about the direction of propagation of light.

The polarized light is lack symmetry about the direction of propagation light.

In unpolarized light the vibrations are confined to any direction.

In polarized light the vibrations are confined to one particular direction.

The unpolarized light is specified as

The polarized light is specified as

Differences between O-ray and E-ray O-ray E-rayThe O-ray obeys the laws of refraction The E-ray does not obeys the laws of refraction The O-ray has vibrations perpendicular to the principal section.

The E-ray has vibrations parallel to the principal section

In negative crystal the velocity light for O- ray is less than the E- ray

In positive crystal the velocity light for E- ray is less than the O- ray

The refractive index of O-ray is same for all angle of incidence

The refractive index of E-ray is always varies with the angle of incidence

engin

eerin

gphy

sics.w

eebly

.com

P.Sr

13. A

GLOBUnit –

reenivasu

Analysis or d

BAL COLLE–I

ula Reddy

detection of

EGE OF ENOPTICS -

M.Sc, (PhD)

f unknown p

NGINEERIpolarisat

Page

polarization

ING &TECtion E

e 9 of 9

n

CHNOLOGYEngineer

Y: YSR DISring Phys

ST. sics

unit 1 optics jntu anantapur

Documents