# Chapter 24

Diffraction Huygens principle requires that the waves spread out after they pass through slits. This spreading out of light from its initial line of travel is called diffraction. In general, diffraction occurs when waves pass through small openings, around obstacles or by sharp edges.

Diffraction from a single slit A single slit placed between a distant light source and a screen produces a diffraction pattern. It will have a broad, intense central band. The central band will be flanked by a series of narrower, less intense secondary bands. Called secondary maxima The central band will also be flanked by a series of dark bands. Called minima

Diffraction Single Slit Fraunhofer Diffraction occurs when the rays leave the diffracting object in parallel directions. Screen very far from the slit Converging lens (shown) A bright fringe is seen along the axis ( = 0) with ) with alternating bright and

dark fringes on each side. Diffraction The results of the single slit cannot be explained by geometric optics. Geometric optics would say that light rays traveling in straight lines should cast a sharp image of the slit on the screen.

Single-Slit Diffraction According to Huygens principle, each portion of the slit acts as a source of waves. The light from one portion of the slit can interfere with light from another portion. The resultant intensity on the screen depends on the direction

Single-Slit Diffraction All the waves that originate at the slit are in phase. Wave 1 travels farther than wave 3 by an amount equal to the path difference (a/2) sin a is the width of the slit If this path difference is exactly half of a wavelength, the two waves cancel each other and destructive interference results. a/2 sin dark = m /2 When y is very small compared to L => sin ~ tan =

y/L ay/L = m => = ay/mL => = ay/m => = ay/mL L Single-Slit Diffraction Destructive interference occurs for a single slit of width a when sin dark = m / a m = 1, 2, 3, Constructive interference occurs for a single slit of width a when sin bright = (m +1/2) / a

m = 0) with , 1, 2, 3, Central is constructive or bright Problem Light of wavelength 650) with nm passes through a single slit of width 0) with .25 mm and forms a diffraction on a screen at 2m away. (a) find the distance of the first and 3rd order dark fringe from the central maximum (b) Find the width of the central maximum. Use small angle approximation

Single-Slit Diffraction The general features of the intensity distribution are shown. A broad central bright fringe is flanked by much weaker bright fringes alternating with dark fringes. The points of constructive interference lie

approximately halfway between the dark fringes. Diffraction Grating The diffracting grating consists of many equally spaced parallel slits. A typical grating contains several thousand lines per centimeter. The intensity of the pattern on the screen is the result of the combined effects of interference and diffraction.

Diffraction Grating The condition for maxima is d sin bright = m m = 0) with , 1, 2, The integer m is the order number of the diffraction pattern. For a diffraction grating

the wavelength of the light is given by = , where m is the order of the bright fringe Section 24.8 Diffraction Grating All the wavelengths are focused at m = 0) with This is called the zeroth order maximum

The first order maximum corresponds to m = 1 Note the sharpness of the principle maxima and the broad range of the dark area. This is in contrast to the broad, bright fringes characteristic of the twoslit interference pattern. Diffraction Grating d = (1/number of lines per unit length in the gratings) Note: if sm => = ay/mL all angle approxim => = ay/mL ation is applicable ie ~ L, each bright and dark fringe will have equal width and will be separated by equal distance from => = ay/mL each other. However, if the above approxim => = ay/mL ation cannot be applied farther the point p is on the screen from => = ay/mL the central

m => = ay/mL axim => = ay/mL um => = ay/mL , larger will be the separation between two nearest bright or dark fringes. We should be able to see this effect in the diffraction grating. Problem Light of wavelength 650) with nm passes through a diffraction grating which has 50) with 0) with 0) with lines/cm. A diffraction pattern is observed on a screen at a distance 150) with cm. At what distance from the central maximum will the first and 2nd order bright fringes occur? Is the small angle approximation applicable here.

Polarization of Light Waves Each atom produces a wave with its own orientation of All directions of the electric field vector are equally possible and lie in a plane perpendicular to the direction of propagation. This is an unpolarized

wave. Section 24.9 Polarization of Light, Cont. A wave is said to be linearly polarized if the resultant electric field vibrates in the same direction at all times at a particular point. Polarization can be obtained from an unpolarized beam by

Selective absorption Reflection Scattering Section 24.9 Polarization by Selective Absorption The most common technique for polarizing light Uses a material that transmits waves whose electric field vectors in the plane are parallel to a certain direction and absorbs waves whose electric field vectors are perpendicular

to that direction Selective Absorption, Final The intensity of the polarized beam transmitted through the second polarizing sheet (the analyzer) varies as I = Io cos2 Io is the intensity of the polarized wave incident on the analyzer. This is known as Malus Law and applies to any two polarizing materials whose transmission axes are at an angle of to each other.

Section 24.9 Polarization by Reflection When an unpolarized light beam is reflected from a surface, the reflected light is Completely polarized Partially polarized Unpolarized It depends on the angle of incidence. If the angle is 0) with or 90) with , the reflected beam is unpolarized.

For angles between this, there is some degree of polarization. For one particular angle, the beam is completely polarized. Section 24.9 Polarization by Reflection, Cont. The angle of incidence for which the reflected beam is completely polarized is called the polarizing angle, p Brewsters Law relates

the polarizing angle to the index of refraction for the material. p may also be called Brewsters Angle. Section 24.9 Problem A light ray which is reflected from glass is found completely polarized when the angle of incidence is 48 degrees. (a) What is the

refractive index of the glass used. (b) What should be the angle of incidence in case of water glass interface for complete polarization of the reflected ray. (Water n = 1.33) Digital Camera Image is formed on an electric device CCD Charge-coupled device CMOS Complementary metal-oxide semiconductor

Both convert the image into digital form. The image can be stored in the cameras memory. Section 25.1 The Eye The normal eye focuses light and produces a sharp image.

Essential parts of the eye Cornea light passes through this transparent structure Aqueous Humor clear liquid behind the cornea Section 25.2 The Size of a Magnified Image When an object is placed at the near point, the angle subtended is a maximum.

The near point is about 25 cm When the object is placed near the focal point of a converging lens, the lens forms a virtual, upright, and enlarged image. Section 25.3 Compound Microscope A compound microscope consists of two lenses. Gives greater magnification than a single lens The objective lens has a short focal length, o<1 cm.

The ocular lens (eyepiece) has a focal length, e, of a few cm. Section 25.4 Refracting Telescope The two lenses are arranged so that the objective forms a real, inverted image of a distant object. The image is near the focal point of the eyepiece. The two lenses are separated by the distance o + e which

corresponds to the length of the tube. The eyepiece forms an enlarged, inverted image of the first image. Section 25.5 Reflecting Telescope, Newtonian Focus The incoming rays are reflected from the mirror and converge toward point

A. At A, a photographic plate or other detector could be placed. A small flat mirror, M, reflects the light toward an opening in the side and passes into an eyepiece. Section 25.5

Exam Review Chapter 21 AC circuit, rms and average values current voltage and power, RC, LR and LCR circuit. Resonance in LCR circuit. Voltage current lead and lag Transformer principle and equation Exam Review Chapter 22 Specular and diffuse reflection Laws of reflection, total internal reflection

Inclined plane mirrors Law pf refraction, Cauchys equation Prism and dispersion, ideas of rainbow Exam Review Chapter 23 Plane mirror, curved mirror, mirror equation Sign convention, ray diagram, Thin lenses, Lens equation, sign convention, ray diagram, lens and mirror aberration.

Exam Review Chapter 24 Interference, double slit equation, general and small angle approximation Sign convention, ray diagram, Thin lenses, Lens equation, sign convention, ray diagram, lens and mirror aberration.

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