Announcements

• HW set 9 due this Monday 11/14; covers Ch 23 and Ch 24.1-4

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after 3PM• or make an appointment

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QUESTIONS? PLEASE ASK!

From last time… Thin Lenses

Converging, diverging Magnification

Lens equation

Remember the sign conventions! (Table 23.3)

Lens maker’s equation

Ray tracing

Converging lenses

Diverging lenses

Chapter 24

Wave Optics

http://www.exploratorium.edu/ronh/bubbles/bubble_colors.html

http://www.ligo.org/

http://upload.wikimedia.org/wikipedia/commons/5/5d/Michelson_Interferometer_Green_Laser_Interference.jpg

http://fuff.org/interference/two_sources_interference.gif

Wave Optics: Coherence and Interference The wave nature of light

Interference, diffraction, polarization

To produce interference – sources must be coherent

(maintain a constant phase w.r.t. each other)

(waves should have identical wavelengths)

Coherent sources Old days: Single Slit +

Double slit Young’s double slit

Today: Lasers!

http://www.black-holes.org/gwa4.html

sciencecity.oupchina.com.hk

Young’s Double Slit Experiment

Light incident on a screen with a narrow slit, So

Light emerging from So arrive at a second screen that contains two narrow, parallel slits, S1 and S2

Light waves emerging from S1 and S2 originate from the same wave front and therefore are always in phase

The light from the two slits form a visible pattern on a screen

The pattern consists of a series of bright and dark parallel bands called fringes

Constructive interference occurs where a bright fringe appears

Destructive interference results in a dark fringe DEMO

Interference Patterns

Constructive interference Constructive

interference(again)

Destructive interference

Question: What is the difference in the path length(distance) that the two waves travel of the above pictures ?

Interference Equations δ = r2 – r1 = d sin θ

assumes the paths are parallel, a very good approximation since L >> d

Bright fringe (constructive interference) δ must be either zero or some integral multiple of the wavelength, λ

δ = d sin θbright = m λ m = 0, ±1, ±2, … m is called the order number

Dark fringe (destructive interference) δ must be an odd half wavelength

δ = d sin θdark = (m + ½) λ m = 0, ±1, ±2, …

Interference Equations The positions of the fringes

can be measured vertically from the zeroth order maximum

y = L tan θ L sin θ L>>d>>λ θ << 1

For bright fringes (constructive interference)

For dark fringes(destructive interference)

dm

bright sin

21sin m

ddark

Phase Changes Due To Reflection An electromagnetic wave

undergoes a 180° phase change upon reflection from a medium of higher index of refraction than the one in which it was traveling

Analogous to a reflected pulse on a string

There is no phase change when the wave is reflected from a boundary leading to a medium of lower index of refraction

Analogous to a pulse in a string reflecting from a free support

Problem 23.13, p 818 Radio waves from a star, of

wavelength 250 m, reach a radio telescope by two separate paths as shown in the figure. One is a direct path to the receiver, which is situated on the edge of a cliff. The second is by reflection off the water. The first minimum of destructive interference occurs when the star is is 25° above the horizon. Find the height of the cliff. (Assume no phase change on reflection.)

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 … DEMO

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 reversal 0 or 2 phase reversals

2nt = (m + ½) constructive destructive

2nt = m destructive constructive

Problem 24.26, p 819 A plano-convex lens with a radius of curvature R = 3.0 m is in

contact with a flat plate of glass. A light source and the observer’s eye are both close to normal, as shown below. The radius of the 50th bright Newton’s ring is found to be 9.8 mm from the center. What is the wavelength of the light produced by the source?

Anti-reflection coatings on solar cells

Answer to 23.13

Answer to 23.26