PH 101: PHYSICS - I [3-1-0]

LA-118

Tuesday-Friday (4.15 -5.15 PM) Dr. Jyoti Prakash Kary

Department of PhysicsNational Institute of Technology

Rourkela[Office:MB 229, Ph: 2732, Email: karjp@nitrkl.ac.in]

TopicsWave optics, Interference, Diffraction, Polarization

Special Relativity, Particle properties of Waves, Waveproperties of Particles, QuantumMechanics.p p

Mark Distributions:Mid Term: 30%

GRADE Distributions: 90 ExMid Term: 30%

End Term: 50%TA: 20%

90 Ex 80 A 70 B 60 C 60 C 50 D 35 P

< 35 FAILTA: ATTENDANCE (5) < 35 FAILTA: ATTENDANCE (5)ASSIGNMENTS (10)

BEHAVIOUR/ATTITUDE (5)

(If you will request me to illegally enhance your marks and attendance : - 10 marks )

Assignments

Assignment-1 Assignment-2 Assignment-3 Assignment-4 Assignment-5

51 2 3 4

Assignments of PH-101

Assignments of PH 101

Assignments of PH 101

Faculty: Dr. J.P. Kar

Name: XYZ

Faculty: Dr. J.P. Kar

Name: XYZRoll no : 0000

Faculty: Dr. J.P. Kar

Name: XYZRoll no : 0000Name: XYZ

Roll no.: 0000Date: 00.00.2012

Roll no.: 0000Date: 00.00.2012

Roll no.: 0000Date: 00.00.2012

Assigned Part

Optics: (i) Interference: Condition for interference, Division of wave

front (two beam interference): Young's double slit experiment fringefront (two beam interference): Young s double slit experiment, fringe

pattern on transverse and longitudinal planes, intensity distribution,

Fresnel's biprism, displacement of fringes; Division of amplitude (two

beam interference): cosine law, Newton's rings experiment, Michelson

Interferometer, fringes of equal inclination and equal thickness. (ii), g q q ( )

Diffraction: Fraunhofer, Fresnel's diffraction, single slit (infinite beam

interference), two and N slits( Grating) Fraunhofer diffraction pattern

and intensity distributionand intensity distribution.

Books

[1] Fundamentals of Optics, F. A. Jenkins, H. E. White, Tata McGraw-Hill (2011)(2011).[2] Optics, A. Ghatak, Tata McGraw-Hill (2011).[3] A Textbook of Optics, N. Subrahmanyam, B. Lal, M. N. Avadhanulu,S. Chand and company (2012).[4] Geometrical and Physical Optics, P. K. Chakrabarti, New CentralBook Agency (2009).g y ( )

WEB REFERENCES1.www. google.co.in1.www. google.co.in2.http://en.wikipedia.org3.www.youtube.com

Optics (light wave)

• Interference

• Diffraction• Diffraction

•Polarization

Why Optics ?

• Windows

• Camera

• Display System

• Microscope and TelescopesMicroscope and Telescopes

• Solar Cell

• Light Emitting Diodes (LED)• Light Emitting Diodes (LED)

• X-ray, LASER

M t i l Ch t i ti (UV Vi ibl t FTIR PL t )• Material Characterization (UV-Visible spectroscopy, FTIR, PL etc)

• Remote Sensing

• Signal processing (optical fiber)

• Bio-medical applications

OpticsOptics is the branch of physics which involves the behaviour

and properties of light including its interactions with matter and theand properties of light, including its interactions with matter and theconstruction of instruments that use or detect it.

G i l i ( i ) Li h ll i f h lGeometrical optics (ray optics): Light as a collection of rays that travelin straight lines and bend when they pass through or reflect fromsurfaces.

Physical optics (wave optics): It includes wave effects such asdiffraction and interference that cannot be accounted for ingeometrical optics.

HistoryHistoryThe word optics comes from the ancient Greek word ὀπτική, meaningappearance or look.

Optics began with the development of lenses by the ancient Egyptiansand Mesopotamians as early as 700 BC.

The ancient Romans and Greeks filled glass spheres with water tomake lenses.

Continued….In Italy, around 1284, Salvino D'Armate invented the firsty, ,

wearable eyeglasses. This was the start of the optical industry ofgrinding and polishing lenses for these "spectacles“ in Venice andFlorence.Florence.

In the early 17th century Johannes Kepler expanded ongeometric optics through reflection by flat and curved mirrors and thegeometric optics through reflection by flat and curved mirrors and theoptical explanations of astronomical phenomena such as lunar andsolar eclipses. He was also able to correctly deduce the role of the

ti th t l th t d d iretina as the actual organ that recorded images.

Until middle of 17th century: light consisted of a stream of corpuscles(Newton)

Middle of 17th century: Wave motion of lighty g1670: Reflection and refraction of light by wave theory (Huygen)1663-1665: Diffraction (Grimaldi, Hooke)1827: Interference (Young, Fresnel)1827: Interference (Young, Fresnel)1873: Electromagnetic nature of light (Maxwell)1901: Quantization of light (Planck)

Light Wave

Light WaveC = λ × f E = h × fC = λ × f

Where

E = h × f

WhereWhere,C = velocity of light (3 ×108 m/s)λ = wavelength of lightf = frequency of light

Where,E = light energyh = Planck’s constant

= 6 626 x 10-34 joule secondf = frequency of light = 6.626 x 10 34 joule.secondf = frequency of light

Long wavelength (Low frequency) Short wavelength (High frequency)

Lights of different color

RED

ORANGELong wavelength (L f )ORANGE

YELLOW

(Low frequency)

GREEN

BLUEBLUE

INDIGO Short wavelength (High frequency)VIOLET (High frequency)

Violet light has higher energy

Interference of lightInterference is a phenomenon in which two coherent lightp g

waves superpose to form a resultant wave of greater or loweramplitude.

Types of interference

interference patterns - Shortcut.lnk Wave Interference - Shortcut.lnk

Types of interference(a) Constructive interference: If a crest of one wave meets a crest ofanother wave, the resultant intensity increases.

(b) Destructive interference: If a crest of one wave meets a trough of( ) ganother wave, the resultant intensity decreases.

Conditions for Interference

[1] The two interfering waves should be coherent, i.e. the phase

difference between them must remain constant with time.

[2] The two waves should have same frequency.

[3] If Interfering waves are polarized, they must be in same state of[3] If Interfering waves are polarized, they must be in same state of

polarization.

[4] The separation between the light sources should be as small as[4] The separation between the light sources should be as small as

possible.

[5] Th di t f th f th h ld b it l[5] The distance of the screen from the sources should be quite large.

[6] The amplitude of the interfering waves should be equal or at least

very nearly equal.

[7] The two sources should be narrow

[8] The two sources should give monochromatic or very nearly

monochromatic, or else the path difference should be very small.

Locus (Mathematics)

In geometry, a locus is a collection of points according to

certain principles.p p

Example: A circle may be defined as the locus of points in a plane (2D)Example: A circle may be defined as the locus of points in a plane (2D)

at a fixed distance from a given point (centre).

Wavefront

In physics, a wavefront is the locus of points having the same

phase (line or curve in 2D, or a surface for a wave propagating in 3D)p ( , p p g g )

2-Dimensional 3-Dimensional

Thomas Young

Screen

Interference of light by

Young's Double Slide Experiment.lnk

* In 1801, Young admitted the sunlight through a single pinhole and thendi d h i li h i h l

division of wavefront

directed the emerging light onto two pinholes.* The spherical waves emerging from the pinholes interfered with each otherand a few colored fringes were observed on the screen.* The pinholes were latter replaced with narrow slits and the sunlight wasreplaced by monochromatic light ( Ex: Sodium lamp, Yellow, 5893 Å)

Interference of Light by Division of WavefrontLight sourceLight source

Single slit

Double slitDouble slit (S1, S2)

Interference pattern on dark film (screen)( )

Intensity distribution

Caluculation of optical path difference between two wavesAs slits (S1 and S2) are equidistant from source (S), the phase of the wave atS1 will be same as the phase of the wave at S2 and therefore, S1,S2 act asS1 will be same as the phase of the wave at S2 and therefore, S1,S2 act ascoherent sources. The waves leaving from S1 and S2 interfere and producealternative bright and dark bands on the screen.

P

x G

O S M

G

2d

H

Let P is an arbitrary point on screen, which is at a distance D from the doubleslits

ScreenYoung’s double slit experiment

slits.2d is the distance between S1 and S2θ is the angle between MO and MP

i th di t b t O d Px is the distance between O and PS1N is the normal on to the line S2PMO bisects S1S2 and GH (i.e. S1M = S2M = GO = HO = d)

Continued…..P

x G

O S M

H

2d

Screen

H

The optical paths are identical with the geometrical paths, if theexperiment is carried out in airexperiment is carried out in air.The path difference between two waves is S2P-S1P = S2NLet S1G and S2H are perpendiculars on the screen and from S2HPt i ltriangle

(S2P)2 = (S2H)2 + (HP)2

= D2 + (x+d)2= D2 + (x+d)2

Continued…..

Since D>>(x+d) (x+d)2/D2 is very smallSince D>>(x+d), (x+d) /D is very smallAfter expansion,

Path difference = S2P-S1P

[(A+B)2 –(A-B)2 = A2 + B2 + 2AB –(A2+B2-2AB) = 4AB]

Continued…..

The nature of the interference of the two waves at P depends simply

on how many waves are contained in the length of path difference

(S2N).

• If the path difference (S2N) contains an integral number of

wavelengths, then the two waves interfere constructively producing a

maximum in the intensity of light on the screen at P.

• If the path difference (S2N) contains an odd number of half-

wavelengths then the two waves interfere destructively and producewavelengths, then the two waves interfere destructively and produce

minimum intensity of light on the screen at P.

Continued…..Thus for bright fringes (maxima),

F d k f i ( i i )For dark fringes (minima),

Let xn and xn+1 denote the distances of nth and (n+1)th bright fringes.

ThenThen,

Continued…..Spacing between nth and (n+1)th bright fringe is

H th i b t ti b i ht f i i thHence, the spacing between any consecutive bright fringe is the same.

Similarly, the spacing between two dark fringes is Dλ/2d,

The spacing between the fringes is independent of n

The spacing between any two consecutive bright or dark fringe is

called the “fringe width” and is denoted by

PROBLEM-1

Q: In an interference pattern, at a point we observe the 12th order

maximum for λ1= 6000 Å. What order will be visible here if the source1

is replaced by light of wavelength λ2= 4800 Å ?

A: In double slit interference, the distance x of a bright fringe from the

t ( d f i ) icentre (zero-order fringe) is

x = (D/2d)nλ, where n = 0,1,2,….

Thus at a given point nλ is constant

Or, n1λ1 = n2λ2

n2 = n1λ1/λ2 = 12 x 6000/4800 = 15

PROBLEM-2

Q: Two straight narrow parallel slits (2 mm apart) are illuminated with

a monochromatic light of wavelength 5896 Å. Fringes are observed at

a distance of 60 cm from the slits. Find the width of the fringes?

A: The interference fringe-width for a double slit is given by

2d 2 0 22d = 2 mm = 0.2 cm,

D = 60 cm,

λ = 5896 Å = 5896 x 10-8 cm

Fringe-width = (60 cmx 5896 x 10-8 cm)/ 0.2 cm = 1.77 x 10-2 cm

PROBLEM-3Q I t lit i t f tt ith λ 6000 Å th d dQ: In a two-slit interference pattern with λ = 6000 Å the zero-order and

tenth-order maxima fall at 12.34 mm and 14.73 mm, respectively. If λ is

Åchanged to 5000 Å, deduce the positions of the zero-order and

twentieth-order fringes, while other arrangements remaining the same.

A: Fringe-width is

with λ = 6000 Å the distance between zero order and tenth orderwith λ = 6000 Å, the distance between zero-order and tenth-order

fringe is 14.73 mm - 12.34 mm = 2.39 mm

F i idth 2 39 /10 0 239Fringe-width = 2.39 mm/10 = 0.239 mm

(Fringe-width)6000/ (Fringe-width)5000 = 6000 Å /5000 Å = 6/5

(Fringe-width)5000 = (Fringe-width)6000 x 5/6 = 0.239 mm x 5/6 = 0.199 mm

Position of zero-order fringe (for λ = 5000 Å) = 12.34 mm

Position of twentieth-order fringe (for λ = 5000 Å)

= 12.34 mm + (0.199 mm x 20) = 16.32 mm