Multiple-Slit Interference

Uniform slits, distance d apart. Light of wavelength . Screen L away “Thin” slits compared to d)

L

y

L >> d then path length difference

between ADJACENT SLITS

sindLadj

Ly

sin Lydd

Ladjadj

2sin

2

2

LyddLadj

adj

2

sin22

For MAXIMUM amplitude of combined waves (“totally constructive interference”), need:

,3,2,1,0

)2(

,4,2,0

m

m

adj

dL

my

Lyd

m

Lyd

m

adj

2)2(

2

Locations of maxima;

Evenly spaced.

Correct for multiple (N > 1) slits

Multiple-Slit Interference Maxima

Multiple-Slit Interference Minima More difficult: need to consider # of slits/sources

2 slits

,5,3, adj

3 slits

Try:

,5,3, adj

get ,232

,32

adj

,234

,34

adj

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N = 2

d = 0.1 mm

= 700 nm

N = 3

d = 0.1 mm

= 700 nm

N = 4

d = 0.1 mm

= 700 nm

N = 5

d = 0.1 mm

= 700 nm

-0.01 -0.005 0.005 0.01

1

2

3

4

5

-0.01 -0.005 0.005 0.01

1

2

3

4

5

-0.01 -0.005 0.005 0.01

1

2

3

4

5

-0.01 -0.005 0.005 0.01

1

2

3

4

5

N = 2

d = 0.1 mm

= 700 nm

N = 3

d = 0.1 mm

= 700 nm

N = 4

d = 0.1 mm

= 700 nm

N = 5

d = 0.1 mm

= 700 nm

-0.01 -0.005 0.005 0.01

1

2

3

4

5

-0.01 -0.005 0.005 0.01

1

2

3

4

5

-0.01 -0.005 0.005 0.01

1

2

3

4

5

-0.01 -0.005 0.005 0.01

1

2

3

4

5

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0

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0

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ConcepTest #61: Consider the interference pattern of four (thin) slits equally spaced a distance d apart:

-0.01 -0.005 0.005 0.01

1

2

3

4

5

Consider the following choices:

1. 0 4. 3/2

2. /2 5. 2

3. 6. none of the above

a) What is the phase difference between adjacent slits for the CENTRAL MAXIMUM?

b) What is the phase difference between adjacent slits for the FIRST SIDE MINIMUM?

c) What is the phase difference between adjacent slits for the SECOND SIDE MINIMUM?

d) What is the phase difference between adjacent slits for the THIRD SIDE MINIMUM?

-0.01 -0.005 0 0.005 0.01

0

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1

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0

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0

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N = 5

d = 0.1 mm

= 700 nm

N = 5

d = 0.09 mm

= 700 nm

N = 5

d = 0.08 mm

= 700 nm

N = 5

d = 0.07 mm

= 700 nm

Diffraction Grating

•Multiple Slit Interference

•LOTS of Slits

•VERY CLOSELY spaced

Example:

•Diffraction Grating from lab

•Laser Vision Glasses

•CD (reflection grating; details next week)

ConcepTest #62: You look at a bright source of white light through a diffraction grating. Looking away from the center, you will see colors. What color will you see closest to the center?

1. Red 4. Green

2. Orange 5. Blue

3. Yellow 6. Violet

Brainstorm: What will you see at the center?

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N = 5

d = 0.1 mm

= 700 nm

N = 5

d = 0.1 mm

= 600 nm

N = 5

d = 0.1 mm

= 500 nm

N = 5

d = 0.1 mm

= 400 nm