physical optics-part 1

7/30/2019 physical Optics-part 1

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PHYSICAL OPTICS

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Interference Youngs Double slit experiment

Diffraction

Dispersion of light and electromagnetic

spectrum

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Contents


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The effects due to superposition of the two

sets of waves is called interference. Types:

Constructive interference

Destructive interference.

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INTERFERENCE


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Constructive interferenceoccurs whenever waves

come together so thatthey are in phase witheach other. This meansthat their oscillations at agiven point are in thesame direction, theresulting amplitude atthat point being muchlarger than the amplitude

of an individual wave. 4

Constructive Interference


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Destructive

interference occurswhen waves cometogether in such a waythat they completelycancel each other out.

When two wavesinterfere destructively,they must have thesame amplitude in

opposite directions. 5

Destructive interference


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Equal or frequency

Superposition at the same time

Superposition at the same place

Travelling in same direction

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Conditions for Interference


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For constructive interference :

Path difference = n

For destructive interference :

Path difference = (n+1/2)

Path difference is the difference in length of the paths covered by

two sets of waves which originate from two different sources and

arrive at the place of superposition of waves

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Conditions for Interference


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Thomas Young first demonstrated interference in

light waves from two sources in 1801 Light is incident on a screen with a narrow slit, So

The light waves emerging from this slit arrive at asecond screen that contains two narrow, parallel slits,

S1 and S2.

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Youngs Double Slit Experiment


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The narrow slits,

S1 and S2 act assources of waves

The wavesemerging fromthe slits originate

from the samewave front andtherefore arealways in phase

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Youngs Double Slit Experiment,Diagram


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The light from the two slits form a visible pattern on a

screen The pattern consists of a series of bright and dark

parallel bands called fringes

Constructive interference occurs where a bright fringe

appears Destructive interference results in a dark fringe

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Resulting Interference Pattern


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The fringe pattern

formed from a YoungsDouble Slit Experimentwould look like this

The bright areasrepresent constructive

interference The dark areas

represent destructiveinterference

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Fringe Pattern


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Constructive

interferenceoccurs at thecenter point

The two waves

travel the samedistance Therefore, they

arrive in phase

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Interference Patterns


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The upper wave has to

travel farther than thelower wave

The upper wave travels onewavelength farther

Therefore, the waves arrive inphase

A bright fringe occurs

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Interference Patterns, 2


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The upper wave travelsone-half of awavelength fartherthan the lower wave

The trough of thebottom wave overlapsthe crest of the upper

wave This is destructiveinterference A dark fringe occurs

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Interference Patterns, 3


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The path difference, , is

found from the tantriangle

= r2 r1= d sin This assumes the paths are

parallel

Not exactly parallel, but avery good approximationsince L is much greaterthan d

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Interference Equations


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For a bright fringe, produced by constructive

interference, the path difference must beeither zero or some integral multiple of thewavelength

= d sin bright= m

m = 0,

1,

2, m is called the order number

When m = 0, it is the zeroth order maximum When m = 1, it is called the first order maximum

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Interference Equations, 2


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The positions of the fringes can be measured

vertically from the zeroth order maximum y = L tan L sin Assumptions

L>>d d>>

Approximation is small and therefore the approximation tan sin

can be used

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When destructive interference occurs, a dark fringe is

observed This needs a path difference of an odd half

wavelength

= d sin dark= (m + )

m = 0,1, 2,

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For bright fringes

For dark fringes

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Interference Equations, final

0, 1, 2brightL

y m md

10, 1, 2

2dark

Ly m m

d


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Determination of wavelength of light

= d/D * (fringe width)

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Uses of Youngs Double SlitExperiment


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A screen is separated from a double slit source by 1.2m.

The distance between two slits is 0.03mm. The secondorder bright fringe is measured to be 4.5cm from centralline. Determine (a) wavelength of light (b) fringe spacing.

Solution:

(a) y= mD/dd=0.03mm , y= 4.5cm, m =2, D=1.2m

= d y/m D = 5.6 *10^-7m

(b) Fringe width = D/d = 0.2m

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Example


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Diffraction is the ability

of light waves to bendaround obstaclesplaced in their path.

Diffraction is thespreading out of wavesthrough an opening oraround the edge of anobstacle.

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Diffraction
http://www.micro.magnet.fsu.edu/primer/java/particleorwave/diffraction/


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Diffraction


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Light Diffraction through clouds

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When light encounters

an obstacle it spreadsout and bends into ageometric shadow.The diffraction pattern

is formed on thescreen.

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Diffraction, contd..

screen


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Diffraction, like

interferencecharacterizes thewave nature oflight.

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Diffraction, contd..


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Water Waves Spread Out behind aSmall Opening


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Diffraction is referred

to as the interferenceof infinite number ofwavelets.

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Significance:


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When the path lengthdifference between rays r1

and r2 is l/2, the two rays willbe out of phase when theyreach P1 on the screen,resulting in destructiveinterference at P1. The pathlength difference is thedistance from the startingpoint of r2 at the center of

the slit to point b.

For D>>a, the path lengthdifference between rays r1and r2 is (a/2) sin q.

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Diffraction by a Single Slit: Locatingthe Minima


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Repeat previous analysis for pairs of rays, each separated by a verticaldistance of a/2 at the slit.

Setting path length difference to

/2 for each pair of rays, we obtain thefirst dark fringes at:

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Diffraction by a Single Slit: Locating theMinima, cont'd

sin sin2 2

a

a

(first minimum)

For second minimum, divide slit into 4 zonesof equal widths a/4 (separation between

pairs of rays). Destructive interference occurswhen the path length difference for each pairis /2.

sin sin 24 2

a

a

(second minimum)


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Dividing the slit into

increasingly larger evennumbers of zones, wecan find higher orderminima:

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(minima-dark fringes)sin , for 1,2,3a m m

Diffraction by a Single Slit:Locating the Minima, cont'd

physical optics-part 1

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