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From last time… Constructive and Destructive Interference Young’s double slit experiment Bright fringe: d sin θ bright = m λ Dark fringe: d sin θ bright = (m+1/2) λ Thin film interference Three different media Constructive and destructive interference equations depend on indices of refraction for each media

Interference in Thin Films Interference is due to the interaction of the waves reflected from both surfaces of the film Ray 1 - phase change of 180° with respect to the incident ray Ray 2 - no phase change with respect to the incident wave Ray 2 travels an additional physical distance of 2t in the film The wavelength λ is reduced by n in the film  the optical path length is 2 n t Constructive interference 2 n t = (m + ½ ) λ m = 0, 1, 2 … takes into account both the difference in optical path length for the two rays and the 180° phase change Destructive interference 2 n t = m λ m = 0, 1, 2 …

Anti-reflection coatings Two phase shifts Constructive interference 2 n t = m λ m = 0, 1, 2 … takes into account both the difference in optical path length for the two rays and both 180° phase changes Destructive interference 2 n t = (m + ½ ) λ m = 0, 1, 2 …

Handling thin films problems Identify the thin film causing the interference Determine the indices of refraction in the film and the media on either side of it Determine the number of phase reversals: zero, one or two Interference is constructive if the path difference is an integral multiple of λ and destructive if the path difference is an odd half multiple of λ NOTE: The conditions are reversed if one of the waves undergoes a phase change on reflection Equation1 phase reversal 0 or 2 phase reversals 2nt = (m + ½) constructivedestructive 2nt = m destructiveconstructive

Diffraction Huygen ’ s principle – light waves spread out after they pass through slits  diffraction Diffraction occurs when waves pass through small openings, around obstacles or by sharp edges A good example was Young ’ s double slit experiment A single slit placed between a distant light source and a screen produces a diffraction pattern broad, intense central band a series of narrower, less intense secondary bands  secondary maxima In between the secondary maxima are a series of dark bands  minima Cannot be explained by geometric optics!!

Single Slit Diffraction Huygen ’ s principle - each portion of the slit acts as a source Light from one side of the slit interferes with light from the other side The resultant intensity on the screen depends on the direction θ Wave 1 travels farther than wave 3 by a path length difference d = (a/2) sin θ If d = /2, the two waves cancel each other and destructive interference results DEMO

Single Slit Diffraction, 2 Divide slit into 1/4, 1/6, … In general, destructive interference occurs for a single slit of width for: m = 1, 2, 3, … Note: doesn ’ t give any information about the variations in intensity along the screen

Single Slit Diffraction, 3 Broad central bright fringe flanked by much weaker bright fringes alternating with dark fringes Points of constructive interference lie approximately halfway between the dark fringes

Problem 24.36, p 819 A screen is placed 50 cm from a single slit that is illuminated with light of wavelength 680 nm wavelength. If the distance between the first and third minima is 3.0 mm, what is the width of the slit?

Polarization of Light Waves Each electron in an atom produces a wave with its own orientation of E Electrons in oscillating sinusoidal motion Unpolarized light - all directions of the electric field vector are equally possible and lie in a plane perpendicular to the direction of propagation of the light 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 In Lasers E unpolarized polarized

The most common technique for polarizing light Your sunglasses!! Uses a material that i) transmits waves whose electric field vectors in the plane are parallel to a certain direction and ii) absorbs waves whose electric field vectors are perpendicular to that direction Polarization by Selective Absorption

Selective Absorption E T = E o cos  I E 2  I T = I o cos 2 θ I o 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 θ to each other

Problem 24.58, p 821 Plane-polarized light is incident on a single polarizing disk, with the direction of E 0 parallel to the direction of the transmission axis. Through what angle should the disk be rotated so the intensity of the light is reduced by a factor of (a) 2, (b) 4, and (c) 6?

Polarization by Reflection

Polarization by Reflection II The angle of incidence for which the reflected beam is completely polarized is called the polarizing angle, θ p Brewster ’ s Law relates the polarizing angle to the index of refraction for the material θ p may also be called Brewster ’ s Angle Brewster ’ s Angle

Polarization by Scattering When light is incident on a system of particles, the electrons in the medium can absorb and reradiate part of the light This process is called scattering An example of scattering is the sunlight reaching an observer on the earth becoming polarized The horizontal part of the electric field vector in the incident wave causes the charges to vibrate horizontally The vertical part of the vector simultaneously causes them to vibrate vertically Horizontally and vertically polarized waves are emitted Why is the sky blue?

Optical Activity Certain materials display the property of optical activity A substance is optically active if it rotates the plane of polarization of transmitted light Also called birefringence Optical activity occurs in a material because of an asymmetry in the shape of its constituent materials

Answer to 23.36

Answer to 23.58