Lecture physics a2 diffraction phd pham tan thi

Diffraction of LightWhen a narrow opaque aperture is placed between a source of light and a screen, light bends around the corners of the aperture.. Comparison: a In an interference patt

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

(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.

No diffraction ; No spreading after passing through slit

Weak diffraction ; Weak spreading after passing through slit

Diffraction

Diffraction of Light

• 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

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 shap e.

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

1 Source and screen are at infinite

distances from slits

Source and screen are at finite distances from slits

2 Incident wavefront on the aperture is plane Incident wavefront on the aperture is either spherical or cylindrical

3 The diffracted wavefront is plane The diffracted wavefront is either

spherical or cylindrical

4 Two convex lenses are required to

study diffraction in laboratory No lenses are required

5 Mathematical treatment is easy Mathematical treatment is complicated

6 It has many applications in

designing the optical instruments

It has less applications in designing the optical instruments

7 The maxima and minima are well

defined

The maxima and minima are not well defined

Difference between Fraunhofer and Fresnel Diffraction

Fraunhofer Diffraction

intensity pattern

Fresnel Diffraction intensity pattern

The maxima and minima are not well defined

The maxima and minima are 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

The rays proceeding in the same direction as the incident rays

focused at O; while those diffracted through an angle θ are focused at

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

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 n

✓ 2⇡

esin✓

◆

= d

Hence the resultant amplitude at P is given by

R = asin

nd 2 sin d2 =

Let ⇡esin✓ = ↵

R = asin↵

sin ↵n =

asin↵

↵ n

↵ n

R = nasin↵

↵

As is small