HL Notes - Diffraction

Agenda:

 _{Diffraction Notes}

 _h/w:

 Read Hamper Chapter 4.8-4.11

 Do exercises 23-27

Objectives

 _{Understand diffraction and draw the}

different diffraction patterns from a

rectangular slit, a sharp edge, a thin tube, and a circular aperture

 _{Appreciate that the first minimum in}

Objectives

 _{Draw the intensity patterns for a single slit of}

finite width and for two slits of negligible width

 _{Show the effect of slit width on the intensity}

Diffraction

 _{The spreading of a wave as it goes past an}

obstacle or through an aperture

 _{Value of the wavelength in comparison to the}

Superposition

..AKA….Interference

One of the characteristics of a WAVE is the ability to undergo INTERFERENCE. There are TWO types.

We call these waves IN PHASE.

Diffraction

Case 1: Wavelength Much Smaller

Than Aperture

Case 2: Wavelength Comparable to

or Bigger than Aperture

 _{Diffraction takes place}

 _{‘Comparable’ means a few times smaller to}

Diffraction Around an Obstacle

 _{Sound, with a much larger wavelength, will}

Case 1: Wavelength Much Smaller

Than Obstacle

Case 2: Wavelength Comparable to

or Bigger than Obstacle

 _{Diffraction takes place}

 _{‘Comparable’ means a few times smaller to}

Diffraction Patterns

 _{When light is}

diffracted, both

constructive

and destructive interference

Diffraction Patterns

 _{Diffraction is}

appreciable if wavelength, λ, is of the same order of

magnitude as the opening, b,

or bigger

b



Diffraction Patterns

 _{Diffraction is}

negligible if wavelength, λ, is much smaller than the

opening, b

b



Huygen’s Principle and Diffraction

 _{Every point on a}

wavefront acts as a secondary source of coherent radiation

 _{Each point forms its}

own wavelet

 _{These wavelets will}

Huygen’s Principle and Diffraction

 _{Because of the}

diffraction angle, wavelet B₁ has a

greater distance to

travel to get to point P than wavelet A₁

 _{This results in the}

Huygen’s Principle and Diffraction

 _{If the difference is}

equal to half a wavelength, the

wavelets are 180° out of phase and they

Huygen’s Principle and Diffraction

 _{If the difference is}

equal to one entire wavelength, the

wavelets are in phase and they form a

Huygen’s Principle and Diffraction

 _{Everything in}

between will show varying levels of constructive and destructive

Huygen’s Principle and Diffraction

 _{Since the two}

triangles in the

diagram are similar triangles, the same interference pattern will result at point P from all pairs of

Huygen’s Principle and Diffraction

 _{If we approximate AP and BP to be parallel since P}

is distant and ACB to be a right angle, then

Huygen’s Principle and Diffraction

 _{Destructive interference occurs when BC is equal}

to one half wavelength, then

Huygen’s Principle and Diffraction

 _{If we divide the slit into 4 segments instead of}

Huygen’s Principle and Diffraction

 _{In general, destructive interference occurs when,}

 _{This equation gives the angle at which minima will}

be observed on a screen (P) behind an aperture of width b through which light of wavelength λ

passes

,...

3

,

2

,

1

sin





n

b

Huygen’s Principle and Diffraction

 _{Since the angle θ is typically small, we can}

approximate sin θ ≈ θ (if the angle is in radians), so the first minima would fall at

 _{And for circular slits the formula becomes}

b







b

Diffraction Patterns

 _{Minima (blank spaces) appear in pairs}

 _{Maxima (bright spaces) appear about halfway}

between minima

 _{Smaller slit means larger central maximum}

b = 2λ _{b = 3λ}

b



Diffraction Patterns

 _{If λ > b, then sin}  _{> 1 which is impossible, i.e.,} 

does not exist

 The central maximum is so wide that the first minima does not exist

 _{If λ ≈ b, then several minima and maxima exist}  _{If λ « b, then sin}   _{o which means}   _{0 which}

Resolution

 _{Diffraction is a way of life}

 _{Diffraction occurs in all lenses, including your}

eye

 _{In diffraction there are maxima and minima}  _{In order to see two objects as two separate}

Rayleigh Criterion

 _{The Rayleigh criterion gives the minimum}

Rayleigh Criterion

 _{The criterion is that the central maximum of one}

Rayleigh Criterion

 _{Two unresolved sources}

Rayleigh Criterion

 _{In diffraction, the first minima for a}

rectangular slit of width b occurs at:

 _{The first minima for a circular slit}

of diameter b occurs at:

 _{Therefore, objects can be resolved}

if their separation angle exceeds



b







b

Rayleigh Criterion

 _{If two objects are separated by a distance s and}

their distance from the observer is d, then their angular separation (in radians) is given by

d

s



Sample Problem

The camera of a spy satellite orbiting at 200km has a diameter of 35 cm. What is the smallest distance this camera can resolve on the surface of the earth? (Assume a wavelength of 500nm)











m

s

x

x

b

d

s

b

d

s

35

.

0

35

.

10

2

10

5

22

.

1

22

.

1

22

.

1

















b

d

s



Microscopes

 _{In microscopes, the object is}

in focus when it is at the focal length of the lens (hence the name)

 _{The condition for resolution}

Microscopes

 _{In practice, f is of the same order of}

magnitude as b so f ≈ b

 _{Therefore, in terms of order of magnitude,}

s ≈ λ

 _{To resolve a small object of size s, the}

Electron Microscope

 _{In order to see an object as small as 0.01nm,}

we can’t use visual light

 _{However, we can make use of the wave}