Interference

EAS-102

11/20/2012

1JITENDRA PAL SINGH

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JITENDRA PAL SINGH

A plano-convex lens of large radius of curvature R is placed on

a plane glass plate with its curved surface downwards and is

illuminated from above with a parallel beam of monochromatic

light. Some of the light is reflected from the upper surface of the

glass plate and some from the lower surface of the lens;

interference thus occurs by division of amplitude, the fringes

being localised in the air gap between the lens and plate.

Ray 1 undergoes a phase change of 180 on

reflection, whereas ray 2 undergoes no phase

change

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Experimental arrangementR= radius of curvature of lens

r=radius of Newton’s ring

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JITENDRA PAL SINGH

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5

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6

Newton's rings in a thin film of diesel oil

on a wet road, seen in white light

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7

QM

C

t

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8

...2

11

,,

)()(

,

,

2

22

22

R

rRR

rRRt

rQMRCQtMO

QMCQMO

CMQIn

RCO

MOCOt

Radius of Newton,s Ring

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9

2

22

1.2

2

1

.2

1

,2

11

2

2

2

2

2

2

R

r

R

rdifferencePath

R

rt

R

rRRRt

RrastermsorderhighergNegelectinR

rRRt

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JITENDRA PAL SINGH

Radius of Bright Fringe

2

)12(

2)12(

2)12(

22)2(

2)2(

2

2

2

2

Rnr

Rnr

Rnr

nR

r

nR

r

Path difference should be an even multiple of λ/2.

i. e.

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11

Diameter of the bright

fringes,

.........3,2,1,)12(

tan2

2.)12(2).12(

2

)12(22

nnD

tconsR

RnRnD

RnrD

n

n

Thus the diameter of bright fringes are proportional to the

square-root of the odd natural numbers.

Ratio of Diameter

for few rings , 646.2:236.2:732.1:1:::

7:5:3:1:::

4321

4321

DDDD

DDDD

Separation between successive rings = 0.732:0.504:0.410

Thus seperation between consecutive bright rings decreases as

the order increases.

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JITENDRA PAL SINGH

Radius of Dark Fringe

....3,2,1,0,

.2

.2

.2

.22

)112(

22)12(

2)12(

2

2

2

2

nRnr

Rnr

RnRnr

nR

r

nR

r

Path difference should be an odd multiple of λ/2.

i. e.

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Diameter of the dark fringes,

.........3,2,1,0,

tan4

2..4

22

nnD

tconsR

RnRnD

RnrD

n

n

Thus the diameter of bright fringes are proportional to the

square-root of natural numbers.

Ratio of Diameter

for few rings , 2:732.1:414.1:1:0:::

4:3:2:1:0:::

4321

4321

DDDD

DDDD

Separation between successive rings = 1:0.414:0.318:0.268

Thus separation between consecutive dark rings also decreases

as the order increases.

Thus, central ringes are broader and peripheral rings are closer.

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JITENDRA PAL SINGH

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NEWTON’S RINGS

Ray 1 undergoes a phase change of 180 on

reflection, whereas ray 2 undergoes no phase

change

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JITENDRA PAL SINGH

An antireflective or anti-reflection (AR) coating is a type

of optical coating applied to the surface of lenses and other optical

devices to reduce reflection.

This improves the efficiency of the system since less light is lost.

In complex systems such as a telescope, the reduction in

reflections also improves the contrast of the image by elimination

of stray light.

This is especially important in planetary astronomy. In other

applications, the primary benefit is the elimination of the reflection

itself, such as a coating on eyeglass lenses that makes the eyes

of the wearer more visible to others, or a coating to reduce the

glint from a covert viewer's binoculars or telescopic sight.

Definition11/20/2012

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JITENDRA PAL SINGH

Many coatings consist of transparent thin film structures with

alternating layers of contrasting refractive index.

Layer thicknesses are chosen to produce destructive

interference in the beams reflected from the interfaces, and

constructive interference in the corresponding transmitted

beams.

This makes the structure's performance change with

wavelength and incident angle, so that color effects often

appear at oblique angles.

A wavelength range must be specified when designing or

ordering such coatings, but good performance can often be

achieved for a relatively wide range of frequencies: usually a

choice of IR, visible, or UV is offered.

Principle11/20/2012

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JITENDRA PAL SINGH

Figure shows the phenomena of interference that lead to

antireflecting coating. In this the refractive index of the coating

material is choosen that it has an intermediate value between

the glass and air.

For example that refractive index of MgF2 is 1.38.

The ray AB is incident on the system and at point B it suffers

reflection on the surface of AR coating (denser medium) and

proceeds along BC. A part of it moves along BD in the same

medium and at D it suffers reflection again at the surface of

denser (glass) and emerges out of along EF in air.

Hence, same phase change occurs in both the rays at

reflection.

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JITENDRA PAL SINGH

AIR μair=1.0

AR Coating, MgF2, μF=1.38

Glass, μglass=1.5

A

B

C

D

E

F

i

r

r

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JITENDRA PAL SINGH

rt

rt

rt

cos2

cos2

22cos2

Reflection at glass/AR coating and AR coating/air bounaries

will produce phase change of π.

Path difference = 2

.2

Total path difference

Term ‘λ’ may be omitted as addition and subtraction of λ

will not affect the path difference.

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JITENDRA PAL SINGH

For normal incidence,

Path difference = 2μ.t

Where, μ and t are refractive index and thickness of AR

coating material respectively.

For condition of destructive interference, 2μ.t= (2n+1).(λ/2)

where, n=0,1,2..

For n=0

2μ.tmin = λ/2

tmin= λ/4 μ

Minimum thickness of the coating required for no reflection at

the centre of visible spectrum (λ = 5.5×10-5 cm)

cmt

cmt

5

min

5

min

10966.0

38.14

105.5

4

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JITENDRA PAL SINGH

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JITENDRA PAL SINGH

If the refractive of thin films coated on glass is higher than that

of glass, then reflectivity of glass surface is increased and the

coating is known as high reflection coating.

Path difference in this case will be given by

For normal incidence2

cos2

rt

22

t

For constructive interference, 2μ.t - (λ/2) =nλ, where, n=0,1,2..

2μ.t = (2n+1)λ/2

For n=0, 2μ.tmin = λ/2

tmin= λ/4 μ

Minimum thickness of the coating required for no reflection at

the centre of visible spectrum (λ = 5.5×10-5 cm)

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JITENDRA PAL SINGH

AIR μa=1.0

HR Coating, μf >μg

Glass, μg=1.5

A

B

C

D

E

F

i

r

r

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JITENDRA PAL SINGH

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JITENDRA PAL SINGH

An intereference filter is a optical system that

transmits a very narrow range of wavelength and

provides a monochromatic beam of light.

They are composed of transparent glass or

quartz substrate on which multiple thin layers of

dielectric material, sometimes separated by

spacer layers

Permit great selectivity

Definition11/20/2012

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JITENDRA PAL SINGH

CONSTRUCTION OF FILTERS

Filter

components

Single Optical

filter

“optical

glue” or

mostly filters

are spatter

Coated in a

vacuum

Interference

Filters

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JITENDRA PAL SINGH

TRANSMISSION DETERMINATION

Constructive and destructive interference

occurs between reflections from various

layers

Transmission determined by :

thickness of the dielectric layers

number of these layers

angle of incident light on the filters

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JITENDRA PAL SINGH

INTERFERENCE FILTERS ADVANTAGES

They can be used as reflectors in two and

three color analysis.

They usually do not themselves produce

fluorescence.

They are available in short pass versions.

They are excellent as primary barrier filters.

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JITENDRA PAL SINGH

INTERFERENCE FILTERS: DISADVANTAGES

Have lower blocking properties

Reduced passing properties

Their reflecting and passing properties

are not absolute, this should be

considered while dealing with multiple

wavelengths

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JITENDRA PAL SINGH

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JITENDRA PAL SINGH

2

1

2

1

E Er12 Er12

Et12 Et12

Er2

12

Ert 1212

Etr 1221

Ett 1221

2112

12211212

or

0

rr

EtrErt

Expts shows that ray

reflected from more

denser medium suffers

a phase change of 1800

glassglass

air air

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JITENDRA PAL SINGH