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Announcements
• HW set 10 due this week; covers Ch 24.5-9 (skip 24.8) and 25.1-3
• Office hours:• Prof. Kumar’s Tea and Cookies 5-6 pm today • My office hours Th 2 -3 pm
• or make an appointment
• Final exam Saturday 4/23, 3 – 5 pm, CUMULATIVE EXAM
• Make-up exam, Wednesday 4/20, 5:10 – 7:00 pm, NPB 1220, CUMULATIVE EXAM
• Always check out http://www.phys.ufl.edu/courses/phy2054/spring11/ for more announcements
QUESTIONS? PLEASE ASK!
From last time…
Constructive and Destructive Interference
Young’s double slit experiment Bright fringe: d sin θbright = m λ
Dark fringe: d sin θbright = (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
Equation 1 phase reversal0 or 2 phase reversals
2nt = (m + ½) constructive destructive
2nt = m destructive constructive
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
2sin2
a
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
2sin2
ma
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
ET = Eo cos
I E2
IT = Io cos2 θ
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 θ to each other
Problem 24.58, p 821
Plane-polarized light is incident on a single polarizing disk, with the direction of E0 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, θp
Brewster’s Law relates the polarizing angle to the index of refraction for the material
θp 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