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- Diffraction
Pham Tan Thi, Ph.D.
Department of Biomedical Engineering
Faculty of Applied Science
Ho Chi Minh University of Technology
- Properties of Light
Effects of Materials on Light
• Transmission
• Reflection
• Refraction
• Absorption
• Total Internal Reflection
• Interference
• Diffraction
• Scattering of Light
• Polarization
- Effects of Materials on Light
Materials can be classified based on how it responds to light incident
on them:
1. Opaque materials - absorb light; do not let light to pass through
2. Transparent materials - allow light to easily pass through them
3. Translucent materials - allow light to pass through but distort the
light during the passage
- Definition of Diffraction
Diffraction is a bending of light around the edges/corners of an
obstacle and subsequently spreading out in the region of geometrical
shadow of an obstacle.
- Diffraction of Light
When a narrow opaque (aperture) is placed between a source of
light and a screen, light bends around the corners of the aperture.
This encroachment of light is called “diffraction”.
For diffraction, the size of the aperture is small (comparable to the
wavelength).
As a result of diffraction, the edges of the shadow (or illuminated
region) are not sharp, but the intensity is distributed in a certain
way depending on the nature of the aperture.
- Difference between Interference and Diffraction
Interference: occurs between waves starting from two (or more) but
finite numbers of coherent sources.
Diffraction: occurs between secondary wavelets starting from the
different points (infinite numbers) of the same waves.
Both are superposition effects and often both are present
simultaneously (e.g. Young’s double slit experiment).
Comparison:
(a) In an interference pattern, the minima are usually almost
perfectly dark while in a diffraction pattern they are not so.
(b) In an interference pattern, all the maxima are of same intensity
but not in the diffraction pattern.
(c) The interference fringes are usually equally spaced. The
diffraction fringes are never equally spaced.
- Diffraction and Hyugen’s Principle
Hyugen’s principle can be used to analyze the diffraction
Diffraction pattern of a razor blade
- What is Huygens’ Principle
Hyugens’ (or Huygens-Fresnel) principle states that every point on a
wavefront is a source of wavelet. These wavelets spread out in the
forward direction, at the same speed as the source wave. The new
waveforms is in line tangential to all the wavelets.
- Diffraction of Light
No diffraction; No spreading after passing
through slit
Weak diffraction; Weak spreading
after passing through slit
Diffraction
- • In Figure 36.3 below, the prediction of geometric optics in
(a) does not occur. Instead, a diffraction pattern is produced,
as in (b).
• The narrower the slit, the broader the diffraction pattern.
- Types of Diffraction
Diffraction phenomena can be classified either as Fresnel
diffraction or Fraunhofer diffraction
The observable difference:
Fresnel diffraction
The viewing screen and the aperture are located close together, the
image of the aperture is clearly recognizable despite slight fringing
around its periphery.
As the separation between the screen and the aperture increases,
the image of the aperture becomes increasingly more structured;
fringes become more prominent.
Fraunhofer diffraction
The viewing screen and the aperture separated by a large distance,
the projected pattern bears little or no resemblance to the aperture.
As the separation increases, the size of the pattern changes but not
its shape.
- Types of Diffraction
- Fresnel’s Diffraction
In the case of Fresnel’s diffraction, the source of light or screen or
usually both are at finite distance from the diffracting aperture
(obstacle)
No lenses are used
The incident wavefront is either spherical or cylindrical
- Fraunhofer’s Diffraction
In the case of Fraunhofer’s diffraction, the source of light or screen
are effectively at infinite distance from the diffracting aperture
(obstacle).
This is achieved by placing the source and screen in the focal
planes of two lenses (require lenses).
The incident wavefront is plane.
- Difference between Fraunhofer and Fresnel Diffraction
No Fraunhofer Diffraction Fresnel Diffraction
Source and screen are at infinite Source and screen are at finite
1
distances from slits distances from slits
Incident wavefront on the aperture is Incident wavefront on the aperture is
2
plane either spherical or cylindrical
The diffracted wavefront is either
3 The diffracted wavefront is plane
spherical or cylindrical
Two convex lenses are required to
4 No lenses are required
study diffraction in laboratory
5 Mathematical treatment is easy Mathematical treatment is complicated
It has many applications in It has less applications in designing the
6
designing the optical instruments optical instruments
The maxima and minima are well The maxima and minima are not well
7
defined defined
- Difference between Fraunhofer and Fresnel Diffraction
Fraunhofer Diffraction Fresnel Diffraction
intensity pattern intensity pattern
The maxima and minima are well defined The maxima and minima are not well defined
- Fraunhofer’s Diffraction at a Single Slit
Let a parallel beam of monochromatic light of wavelength λ be
incident normally on a narrow slit of width AB = e.
Let diffracted light be focused by a convex lens L on a screen XY
placed in the focal plane of the lens.
The diffraction pattern obtained on the screen consists of a central
bright band, having alternate dark and weak bright bands of
decreasing intensity on both sides.
- Fraunhofer’s Diffraction at a Single Slit
In terms of wave theory, a plane wavefront is incident on the slit AB.
According to the Huygens’ principle, each point in AB sends out
secondary wavelets in all directions.
The rays proceeding in the same direction as the incident rays
focused at O; while those diffracted through an angle θ are focused at
P.
Let us find the resultant intensity at P.
Let AK be perpendicular to BP. As the optical paths from the plane AK
to P are equal, the path difference between wavelets from A to B in the
direction θ is BK = AB sinθ = e sinθ
The corresponding phase difference = (2π/λ)e sinθ
Let the width AB of the slit be
divided into n equal parts. The
amplitude of vibration at P due to
the waves from each part will be
the same (= a)
- Fraunhofer’s Diffraction at a Single Slit
The phase difference between the waves from any two consecutive
parts is
✓ ◆
1 2⇡
esin✓ =d
n
Hence the resultant amplitude at P is given by
nd ⇡esin✓
asin 2 asin
R= d
= ⇡esin✓
sin 2 sin n
⇡esin✓
Let =↵
asin↵ asin↵ ↵
R= ↵ = ↵ As is small
sin n n n
nasin↵
R=
↵
nguon tai.lieu . vn
