WAVE OPTICS & LASER

WAVE OPTICS & LASERInterference

Air-Wedge – Theory and Applications

LASER

Types of LASER

Nd:YAG LASER, CO2 LASER, Semiconductor LASER (homojuntion)

Application : Holography

Fiber Optics – Principle

Types of Optical Fibers

Fiber Optics Communication System

WAVE OPTICS

Wave Optics deals with different optical phenomena

Interference

Diffraction

Polarisation

INTERFERENCE

A phenomenon in which two waves superpose to form a

resultant wave of greater amplitude or lower amplitude

Interference effects can be observed with all types of

waves

Light waves

Radio waves

Acoustic waves

Surface water waves

Matter waves

Path difference and phase difference will

be meaningful for waves of same

frequency

They are used to determine constructive

and destructive interference in waves

Path Difference and Phase Difference

Path difference (measured in terms of wavelength)

Actual measurable difference in distance that two waves travel from a source to a common point

Path difference between the red and blue wave = λ/ 4

Phase difference (measured in radians)

Difference in the phases of the two sinusoidal waves of same frequency

The blue wave leads the red wave by a phase difference of π/2 (90 degrees)

At time t = 0

Blue wave displacement = 0

Red wave displacement = – A

Path Difference and Phase Difference

At π/2

Blue wave has maximum displacement = + A

Red wave displacement = 0

Blue wave is leading by a phase difference

of π/2 and path difference of λ/4

One oscillation is completed in 2π radians which is equivalent to wavelength λ

(Path difference of one wavelength (λ) is equal to phase difference of 2π radians)

Waves follow different paths from the slits to a common point on a screen

(a) Destructive interference One path is a half wavelength longer than the otherThe waves start in phase but arrive out of phase

(b) Constructive interferenceOne path is a whole wavelength longer than the otherThe waves start out and arrive in phase

PD = 5λ – 4.5λ = 0.5λ = ½ λ

PD = 5.5λ – 4.5λ = λ

Constructive Interference

OPTICAL INTERFERENCE

Formation of bright and dark bands resulting from the

super-position of two coherent light waves

Coherent light waves

Light waves have

same wavelength

same amplitude

constant phase difference

Constructive Interference (Bright band)

Path difference = n λ

Phase difference = n 2π

Destructive Interference (Dark band)

Path difference = (2n – 1) λ/2

Phase difference = (2n – 1)π

Optical Interference

Band Width or Fringe Width

Distance between two successive bright bands or dark bands

d

D λ β

pattern ceinterferen producing sourcescoherent between distance - d

screen and sources obetween tw Distance - D

Optical Interference

To obtain clear and broad interference bands

(i) Wavelength of light should be larger

(ii) Light sources should be closer and narrower

(iii) Distance between the screen and the coherence sources should be larger

OPTICAL PATH LENGTH

Product of the geometric length (d) of the path light follows through a system and the refractive index (μ) of the medium through which it propagates

OPL = μ d

Polarisation

Optical phenomenon in which the light vibrations are restricted to take

place in a single plane

An ordinary light is unpolarised light since it can vibrate in all directions in

a plane perpendicular to the direction of propagation of light

Interference at a Wedge-Shaped Film

ABC - A wedge shaped film of refractive index (μ) with very small angle

A parallel beam of monochromatic light is incident on the upper surface

The surface is viewed by reflected light through a travelling microscope

Alternate dark and bright bands can be observed

Interference at a Wedge-Shaped Film

An air wedge is formed by two plates of glass separated at one end

No phase change

180o phase change

Interference effect is between light reflected from the bottom surface of the top

plate and light reflected from the top surface of the lower plate

Bottom of the upper plate → glass-to-air boundary (μglass > μair)

No phase change upon reflection

Top of the lower surface → air-to-glass boundary (μair < μglass)

There is a 180° phase change upon reflection from this surface

Interference at a Wedge-Shaped Film

Point P will appear dark and a dark

band will be observed across the

wedge, if

2/)12(2/2 nμt

nμt 2

Point P will appear bright and bright band will be observed across the

wedge, if

nμt 2/2

2/)12(2 nμt

Interference at a Wedge-Shaped Film

If the nth dark fringe is formed at P

nμt 2

θxor t θx

t1

1

nλθx2 1

Similarly, for the (n+1)th dark band which is formed at Q at a distance

x2 from A

1)λn(θx2 2

Interference at a Wedge-Shaped Film

So, if we consider any two consecutive bright fringes, β will be the same

nλθx2 1

Fringe width (β)

)λ1n(θx2 2

λ)xθ(x2 12

2

λxx 12

Interference at a Wedge-Shaped Film

A wedge shaped air film can be obtained

by inserting a thin piece of paper or hair

or thin wire between two glass plates

1For air film x

tθ

2t

λx

2

λ

t – thickness of paper or hair or thin wire

x – distance from the edge to the paper or hair or

thin wire

2

λxt

Thickness of a paper or wire or hair(1) A wedge shaped film is obtained

by inserting a thin paper or thin

wire or hair between two parallel

glass plates (optical flats)

(2) Sodium vapour lamp is used as

the light source

(3) Light is incident on the glass plate

inclined at 45⁰ to the horizontal

(4) Glass plate makes the light to fall normally on the optical flats by reflection

(5) By adjusting the distance between the microscope objective and optical flats,

we can get the interference fringes in the microscope eye piece

Thickness of a paper or wire or hair(6) By coinciding one of the bright

fringes with the vertical crosswire,

the reading is noted in the

horizontal scale of microscope

(7) After crossing of five bright fringes,

once again the reading is noted

(8) The value of fringe width is

calculated

(9) Distance “x” from the edge where the two plates touch each other to the

paper or thin wire is measured

(10) Then the thickness t can be calculated from the formula2

λxt

Testing of flatness of a surface

Not smooth surface

Smooth surface

Incident light

Incident light

Testing of flatness of a surface

Wave Optics

InterferenceBright BandPath Diff = nλPhase Diff = n2π

Dark BandPath Diff = (2n-1)λ/2Phase Diff = (2n-1)π

Air Wedge shaped film

Thickness of thin sheet or wire or hair

Testing of Flatness of a surface