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: Opaque materials - absorb light; not let light to pass through Transparent materials - allow light to easily pass through them 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 distances from slits Incident wavefront on the aperture is Incident wavefront on the aperture is plane either spherical or cylindrical The diffracted wavefront is plane The diffracted wavefront is either spherical or cylindrical Two convex lenses are required to study diffraction in laboratory No lenses are required Mathematical treatment is easy Mathematical treatment is complicated It has many applications in designing the optical instruments The maxima and minima are well defined It has less applications in designing the optical instruments The maxima and minima are not well defined Source and screen are at finite distances from slits Difference between Fraunhofer and Fresnel Diffraction Fraunhofer Diffraction intensity pattern The maxima and minima are well defined Fresnel Diffraction intensity pattern 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 n ✓ 2⇡ esin✓ ◆ =d Hence the resultant amplitude at P is given by R= Let ⇡esin✓ asin sin nd d = asin sin ⇡esin✓ ⇡esin✓ n =↵ asin↵ asin↵ R= ↵ ↵ = sin n n nasin↵ R= ↵ ↵ As is small n ... 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... 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... 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