Lecture Physics A2: Diffraction - PhD. Pham Tan Thi

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Lecture Physics A2: Diffraction - PhD. Pham Tan Thi present the content properties of light, effects of materials on light, definition of diffraction, diffraction of light, diffraction and Hyugen’s principle, Fresnel’s diffraction,...

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Nội dung Text: Lecture Physics A2: Diffraction - PhD. Pham Tan Thi

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= ↵