Announcements: Review quiz and Exam 2

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Spencer Shields
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1 Announcements: Review quiz an Exam Review Quiz on Friay, Oct. 31st, 014, in class Turn in the Quiz at the en o class or extra creit (up to 50 points). Open book quiz. Bring ormula sheet, scientiic calculator, book, notes, etc. Exam : Wenesay, Nov. 5th, 014, in class Close book exam, Material covere: Hecht Ch (material covere in lectures up to an incluing lecture no. 5) Bring ID, ormula sheet (1 letter-size piece o paper, both sies), scientiic calculator, pen/pencil

2 Chapter 9 Intererence Phys 3 Lecture 4 Intererometers Waveront-splitting intererometers Amplitue-splitting intererometers Mirrore intererometers

Optical path length ierence: r r 1 = a sin θ = ay/s ( I s>> a, s>> y ) Position o bright ringes: asin m m m a s m a m

3 Waveront-splitting intererometers Young s experiment (1801) Young s originality: Obtaining spatially coherent light rom a pinhole, an splitting the waveront o the spatially coherent light with two pinholes. Optical path length ierence: r r 1 = a sin θ = ay/s ( I s>> a, s>> y ) Position o bright ringes: asin m m m a s m a m = 0, ±1, ±, is the orer number. s Space between ringes: y a Intensity istribution o the ringes: y m m a s I k( r1 r ) 4I0 cos 4I0 cos 4I0 cos ay s ay/s

4 Eects o inite coherent length: Light rom each slit has a coherent length l c. For sunlight l c 3. The waves rom two slits can only interere i r r 1 <l c. The contrast o the ringes egraes when the amount o the overlap between uncorrelate wavegroups increases. l c A A' B B' P

5 Other Waveront-splitting intererometers Lloy s mirror intererometer: Intererence between light rom source S an its image S ' in the mirror. Glancing incience causes a phase shit o. The ringes are complementary to Young s. S a S' s y I 4I0 sin ay s

6 Phase shits in relection (Fresnel eqns.) n i < n t external n t < n i internal 180 phase shit or all angles Interesting phase above critical angle Incience angle Incience angle 180 phase shit or angles below Brewster's angle; 0 or larger angles Incience angle Incience angle

7 Fresnel s ouble mirror intererometer Other Waveront-splitting intererometers Fresnel s ouble mirror: Slits S 1 an S act as virtual coherent sources. They are images o slit S in two mirrors. S 1 M 1 S Shiel r 1 P y = r r 1, y = s/a a s S r M

8 Fresnel ouble prism: Intererence between light reracte rom the upper an the lower prisms. Two virtual coherent source S 1 an S are prouce by the prisms. a S S 1 Question: Where are S 1 an S? S

9 Chapter 9 Intererence Phys 3 Lecture 5 Intererometers Waveront-splitting intererometers Amplitue-splitting intererometers Mirrore intererometers

10 Intererence in thin ilms

Incient ray relects (m+1) times in the ilm an combines with the relecte

11 Intererence in thin ilms Incient ray relects m times in the ilm an combines with the transmitte beam. Incient ray relects (m+1) times in the ilm an combines with the relecte beam Intererence epens on the path ierence; result epens on, or color o light Phase o EM wave can change in relection!

12 Double-beam intererence in thin ielectric ilms: ringe o equal inclination Optical path ierence: AB BC n AD n 1 AB BC / cos t AD AC sin Snell s law i n cos Note: or < 30 0 external/internal relection lea to relative phase shit o : Phase ierence: k 0 relection t 4n 0 cos t relection 4 0 n n sin 1/ i relection 1

13 Intererence in thin ilms 4n 0 cos t relection 4 0 n n sin 1/ i relection 1 Maxima: = m Minima: =(m+1) Special case: normal incience = 0: 4n 0 relection

14 Example Blue light = 500 nm incient normally on a thin ilm o glass on top o plastic. The intererence is: (1) constructive () estructive (3) neither t=3.333 m 1 n=1 (air) n glass =1.5 n plastic =1.8 Solution strategy: 1. Determine phase shit ue to the optical path ierence. Determine phase shit ue to relections 3. Analyze the total phase shit in terms o or phase shit air Reminer: water No phase change

15 Example Blue light = 500 nm incient normally on a thin ilm o glass on top o plastic. The intererence is: (1) constructive () estructive (3) neither Solution: 1. Path:. Relection: 4n glas s 0 relection t=3.333 m 1 40 relection 0, relection 1, relection n=1 (air) n glass =1.5 n plastic = Total path ierence: 40 0 CONSTRUCTIVE What i there woul be air on the bottom o the glass?

16 Fringes o equal thickness (Fizeau) Thickness: x Near normal incience: maxima: 1 m x m 1/ x m Distance between maxima: x m

17 Fringes o equal thickness: examples 1 m

18 Newton s rings Why is center ark? x R R x R maxima: = (m+½) x m 1 R

Newton s rings Isaac Newton 1643 177 Newton about Newton s rings: "I orbore to treat o these Colors, because they

19 Newton s rings Isaac Newton Newton about Newton s rings: "I orbore to treat o these Colors, because they seeme o a more iicult Consieration, an were not necessary or establishing the Properties o Light there iscourse o."

20 Intererence: reaing CD Lan: no intererence Pit: estructive intererence

21 Comparison o various optical storage meia

22 Summary: Amplitue-splitting intererometers Dielectric ilms ouble-beam intererence Application: Optical coating reuces or enhances relection o optical evices through thinilm intererence eects. Fringes o equal inclination Consier the irst two relections (others are weak). Optical path length ierence: n ( AB BC) n AD n n1 cos t t AC sin n n sin t n cos cos t i 1 n n cos t 1 cos tan sin t t Phase ierence: Assume n >n 1, n >n. There is a phase shit o between external an internal relections (when the incient angle is not large). 4n k cost Bright spot: cost (m 1) Dark spot: cost m 4 4 i S i A D t B C P n 1 n n

Extene source: All rays incline at the same angle arrive at the same point. Fringes o equal inclination: Arcs centere on the perpenicular rom the eye to the ilm.

23 Extene source: All rays incline at the same angle arrive at the same point. Fringes o equal inclination: Arcs centere on the perpenicular rom the eye to the ilm. Haiinger ringes: The ringes o equal inclination viewe at nearly normal incience. Concentric circular bans. sin n cost Fringes o equal thickness Fizeau ringes: Contours rom a non-uniorm ilm when viewe at nearly normal incience. Thickness: = x Intererence maximum: n m = (m + ½) m (m 1), 4 Fringe space: x = / x m (m 1) 4 x n 1 n n

24 Newton s rings: Intererence pattern rom air ilm between glass suraces. x Thickness: Bright rings: n m = (m + ½) Dark rings: R x R x ) ( R m x m m m 1, 4 1) ( R m x m sin x R n

Chapter 10. Interference of Light

Chapter 10. Interference of Light Last Lecture Wave equations Maxwell equations and EM waves Superposition of waves This Lecture Two-Beam Interference Young s Double Slit Experiment Virtual Sources Newton