Conditions for interference Young's double slit experiment ..., Study notes of Physics

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 Conditions for interference

 Young’s double slit experiment

 Intensity distribution of the interference

pattern

 Phasor representation

 Reflection and change of phase

 Interference in thin films

 If two waves have a definite phase

relationship then they are coherent.

 Otherwise, they are incoherent (ex: two

light bulbs).

 For Interference:

 The sources must be coherent.

 The sources should be monochromatic.

  r 2 (^)  r 1  d sin

  d sin  m 

  



  

    2

1 d sin m m  0 ,  1 , 2 ,...

L d

d



 sin  tan y  L tan   L sin

m d

L ybright

 

 

  

   2

1 m d

L ydark



Constructive interference

Destructive interference

An interference pattern is formed on a screen by shining a planar wave on

a double- slit arrangement (left). If we cover one slit with a glass plate

(right), the phases of the two emerging waves will be different because

the wavelength is shorter in glass than in air. If the phase difference is

180 °, how is the interference pattern, shown left, altered?

1. The pattern vanishes.

2. The bright spots lie

closer together.

3. The bright spots are

farther apart.

4. There are no changes.

5. Bright and dark spots

are interchanged.

 Interference depends on the relative phase of the two

waves.

 It also depends on the path difference between them.

 The resultant intensity at a point is proportional to the

square of the resultant electric field at that point.

 

2 I  E 1  E 2

2 2

2 not E 1 (^)  E

• A wave traveling from a medium of

index of refraction of n 1 towards a

medium with index of refraction of n 2

undergoes a 180° phase change

upon reflection if n 2 > n 1 and no

phase change if n 2 < n 1.

• The wavelength of light  n in a

medium with index of refraction n is

given by,  n =  / n.

t m   n

(^2)  

  

   2

1 2 nt m

For constructive

interference

m = 0,1,2,…

2 nt  m 

For destructive interference

m = 0,1,2,…

r  m  R / n

r   m  1 2   R / n

For constructive

interference

For destructive

interference

Since both paths have the same phase change at the interfaces, take only the path differences into account.

t

tm m   n 

  

   2

1 2

n

tm m

  

  

   2

1 2

 

nm

nm

n

t 94. 8

41. 45

550

4

  



For destructive interference

Example:  = 550 nm, no

reflection

Destructive interference at the tip because of

180 ° phase change for the front surface and no

phase change for the back surface.

2 ntm  m 

For destructive interference

 

  

 ntm   m 2

1 2

For constructive interference

 An interferometer can measure

changes in length very

accurately by observing the

fringes.

 The phase difference is due to

the path length difference

between the two arms of the

interferometer.

 If a thin material is inserted in

one arm, the change in the

number of fringes is the change

in the path difference.

  2  d 1  d 2 

 Reading Assignment

 Chapter 38 - Diffraction and Polarization

 WebAssign: Assignment 15