09 Diffraction.pptx

Huygens Principle

point sources for the production of spherical secondary waves, called

wavelets, which

propagate outward with speeds characteristic of waves in that medium.

After some time has elapsed, the new position

of the wave front is the surface tangent to the

Huygens Principle

point sources for the production of spherical secondary waves, called

wavelets, which

propagate outward with speeds characteristic of waves in that medium.

After some time has elapsed, the new position

of the wave front is the surface tangent to the

Sound Waves

Light Waves

Young’s Experiment

In Young’s experiment, light from a monochromatic source falls on two slits, setting up an interference pattern analogous to that with water waves.

Light

source S₁

The Superposition Principle

• The resultant displacement of two simul-taneous waves (blue and green) is the algebraic sum of the two displacements.

The superposition of two coherent light waves results in light and dark fringes on a screen.

• The composite wave is shown in yellow.

Conditions for Bright Fringes

Bright fringes occur when the difference in path DL

is an integral multiple of one wave length l.

L₁

L₂

L₃

L₄

l l l

Path difference

DL = 0, l , 2l, 3l, …

Bright fringes: DL = nl, n = 0,

Conditions for Dark Fringes

Dark fringes occur when the difference in path DL

is an odd multiple of one-half of a wave length l/2.

p₁

p_{2 l}

l

p₃

p₃

n = odd

n = 1,3,5 …

Dark fringes: _L

2

l

2

p n l

D 

1, 3, 5, 7, . . .

2

p n

l

n

m = 1

d

m = 2

d

θ

m = 3

d

θ

Bright

mλ d

θ

L

X_m

θ

tan(θ) = x_m/L

The Diffraction Grating

A diffraction grating consists of thousands of

parallel slits etched on glass so that brighter and sharper patterns can be observed than with

Young’s experiment. Equation is similar.

A diffraction grating consists of thousands of

parallel slits etched on glass so that brighter and sharper patterns can be observed than with

Young’s experiment. Equation is similar.

d sin q

q

d

d sin q  nl

The Grating Equation

The grating equation:

d = slit width (spacing)

l = wavelength of light

q = angular deviation

m = order of fringe

2nd order 2l4l 6l l2l3l 1st order m m

sin

1, 2, 3, ...

d

Diffraction Grating

θ

d

θ

λ

d sin(

∙

θ) = λ

d

Diffraction Grating

θ θ

2λ

d

θ

θ

Diffraction Grating

Single Layer of Blood Cells

.439 m

.055 m

Example 2: Light (600 nm) strikes a grating ruled with 300 lines/mm. What is the angular deviation of the 2nd order

bright fringe?

300 lines/mm

n = 2

To find slit separation, we take reciprocal of 300 lines/mm:

Lines/mm  mm/line

1

0.00333 mm/line

300 lines/mm

d





3

mm 10 m

0.00333

line 1 mm

d















3 x 10 m

Example (Cont.) 2: A grating is ruled with 300 lines/mm.

What is the angular deviation of the 2nd _{order bright fringe?}

q₂ = 21.10

q₂ = 21.10

Angular deviation of second order fringe is:

300 lines/mm

n = 2

l = 600 nm

-9

-6

2

2(600 x 10 m)

sin

;

3.33 x 10

d

l

q





sin

q



0.360

sin

2

d

q



n

l

n



-6

3 x 10 m

A compact disk acts as a diffraction grating. The colors and intensity of the reflected light depend on the

http://farm2.staticflickr.com/1399/5309770206_253e2e87b4_z.jpg

½a

a

½ a sin(

∙

θ) = ½

λ

θ θ

Single Slit Diffraction

Destructive Interference

½ a

a

θ

½ a sin(

∙

θ) =

3

/2 λ

Single Slit Diffraction

Destructive Interference

θ

1

/

2

a sin(

∙

θ) =

/

λ

Single Slit Diffraction

m=

1

,

3

,

5

. . .

Destructive

1

/

2

a sin(

∙

θ) =

/

λ

/

2

a sin(

∙

θ) =

/

λ

http://laser.physics.sunysb.edu/~mkorn/lecture/single_slit_diffraction.JPG

Single Slit Diffraction

Equally Spaced Dark Spots

Decreasing Intensity

m=1 m=3

The "lenses" consist of two layers of cardboard with a small hole about 6

millimeters (0.24 in) in

diameter punched through both layers. The user views objects through the holes. A feather is embedded

between the layers of each lens. The vanes of the

feathers are so close together that light is

diffracted, causing the user to receive two slightly

Example 3: Monochromatic light shines on a single slit of

width 0.45 mm. On a screen 1.5 m away, the first dark fringe is displaced 2 mm from the central maximum. What is the wavelength of the light?

q

x = 1.5 m

y

a = 0.35 mm

l = ?

l = 600 nm

sin

a

l

q



y

sin

tan

;

;

x

y

ya

x

a

x

l

q



q





l



(0.002 m)(0.00045 m) 1.50 m

Diffraction for a Circular Opening

Circular diffraction

D

The diffraction of light passing through a circular opening produces circular interference fringes

that often blur images. For optical instruments, the problem increases with larger diameters D.

The diffraction of light passing through a circular opening produces circular interference fringes

Summary

Bright fringes: Dark fringes:

Young’s Experiment: Monochromatic light falls on two slits, producing

interference fringes on a screen.

x

y

d sin q

s₁

s₂d q p₁

p₂

,

0, 1, 2, ...

dy

n

n

x



l



2

,

1, 3, 5...

Summary (Cont.)

The grating equation:

d = slit width (spacing)

l = wavelength of light

q = angular deviation

n = order of fringe

sin

1, 2, 3, ...

Summary (Cont.)

Pattern Exaggerated

Relative Intensity

Interference from a single slit of width

a

Interference from a single slit of width

a

Dark Fringes: sin

n

n

1, 2, 3, . . .

a

l

Find each of the following using both 1st order and 2nd order locations. Find the aperture of a pin hole

Find the wavelength of the green and

violet lasers. (Find % E of D)

Find the diameter of your red blood cells.

Find the aperture of a single slit and the separation of double slits.

1.

2.

4. 3.