PHY 114 A General Physics II 11 AM-12:15 PM TR Olin 101

Transcription

1 PHY 4 A General Physics II AM-:5 PM TR Olin 0 Plan for Lecture (Chapter 37): Wave properties of light. Interference of two electromagnetic waves. Interference of electromagnetic waves in thin films 4//0 PHY 4 A Spring 0 -- Lecture

2 4 th exam will be offered during the week of April 3 rd. 4//0 PHY 4 A Spring 0 -- Lecture

3 Upcoming event: Society of Physics Students Keynote address Friday April 0, 0 8 PM in Brendle recital Hall Professor William Phillips from NIST and UMD Time, instein, and the Coolest Stuff in the Universe Dr. Phillips was awarded the 997 Nobel Prize in Physics : for development of methods to cool and trap atoms with laser light The 997 prize was shared with Steven Chu of Stanford University and Claude Cohen-Tannoudji of the cole Normale Superieure, Paris. 4//0 PHY 4 A Spring 0 -- Lecture 3

4 3 rd exam solutions Solutions posted on web xam review session?? Would you like to attend an exam review session? (A) yes (B) no If you would like a review session, can you meet (A) Today at PM (here) (B) Tomorrow at PM Olin 07 (C) Tomorrow at PM Olin 07 (D) Other? Similar problems may appear on final exam 4//0 PHY 4 A Spring 0 -- Lecture 4

5 Comment about functions and derivatives: Current as a I( t) 0. di dt 0.00 function of ( 0.0t ) time (in units of Amps) : Charge as a function of time : q(t) dq dt q 0 e q 0 t / τ t e τ / τ 4//0 PHY 4 A Spring 0 -- Lecture 5

6 Webassign hint: 4//0 PHY 4 A Spring 0 -- Lecture 6

7 4//0 PHY 4 A Spring 0 -- Lecture 7 q 0 Note : Solve for Working backwards : < + q p f q p p p f q p p d q + Solve for Continuing analysis: p q

8 Another example (#36.0 in your text): 4//0 PHY 4 A Spring 0 -- Lecture 8

9 From previous lecture: Diverging lens: virtual image of face smaller Converging lens: virtual image of face larger 4//0 PHY 4 A Spring 0 -- Lecture 9

10 Wave phenomena associated with light Plane polarized electromagnetic wave at an instant of time: x, t) y ( π sin ϕ Superposition of tot y ( x, t) y ( x, t) + ( x vt) + two electromagnetic waves (electric field portion) y ( x, t) k tot y ( x, t) sin sin π π + ( x vt) sin ( x vt) ϕ ( x vt) + ϕ cos π + ϕ 4//0 PHY 4 A Spring 0 -- Lecture 0

11 tot y ( x, t) Superposition (continued) sin sin π π + π ϕ ( x vt) sin ( x vt) ( x vt) + ϕ cos + ϕ Note that this sin( A) + sin( B) Squared magnitude : Intensity of I I S avg 4 cµ result follows from the trigonometric identity : A + sin the M waves : 0 ϕ cos B cos sin( A) + sin( B) I 4I cos A B A + B cos tot cµ 0 4//0 PHY 4 A Spring 0 -- Lecture 4sin A B ϕ Constant in time Time average /

12 xample: ϕ0.5 rad -- plotting snapshot of M wave xample: ϕ3 rad plotting snapshot of M wave Intensity as a function of ϕ: ϕ/(π) 4//0 PHY 4 A Spring 0 -- Lecture

13 Summary of interference phenomena due to two or more electromagnetic waves which combine at a give point P with path lengths r and r and fixed frequency f. πr ± πr ( P, t) sin πft sin πft Trig identity : sin A + sin B sin ( ( A + B) ) cos( ( A B) ) I 4I { cos ( ( A B) )} sin A sin B π π 0 cos ( ( A + B) ) sin( ( A B) ) I 4I { sin ( ( A B) )} π π ( A B) π π 0 ( A B) 4//0 PHY 4 A Spring 0 -- Lecture 3 π π

14 Two examples of superposed radiation: Interference from refraction and reflection of thin films Young s double slit 4//0 PHY 4 A Spring 0 -- Lecture 4

15 Young s double slit geometry: Mathematical analysis of bright fringes: ( P, t) πr sin π sin πft + ( r + r ) π( r r ) intensity ima occur for πft r r δ d sin θ πr sin πft cos ( r r ) π mπ d sin θ m 4//0 PHY 4 A Spring 0 -- Lecture 5 δ

16 Intensity pattern at screen for double slit: I S av ( r r ) 4 π 4 cos cos μ c μ c 0 0 πd sin θ I 4//0 PHY 4 A Spring 0 -- Lecture 6

17 Diffraction pattern from a plane wave incident on a double slit: ( P, t) πr sin π sin πft + ( r + r ) π( r r ) intensity ima occur for πft r r δ d sin θ πr sin πft cos ( r r ) π mπ d sin θ m 4//0 PHY 4 A Spring 0 -- Lecture 7 δ

18 Summary of results: Constructive interference : d sin θ m Image on screen : y m D d 4//0 PHY 4 A Spring 0 -- Lecture 8

19 Interference in thin films x, t) y ( π sin ϕ c v ; n ( ) x vt + c nf v c ; n c n f v c ; n c n f v 3 c ; 3 n 3 c n f 3 Interfering reflected light Interfering transmitted light 4//0 PHY 4 A Spring 0 -- Lecture 9

20 Interference between reflected waves: Recall -- the behavior of a plane-polarized electromagnetic wave near the surface of two materials: Periodic waves: B k k sin sin ω ω k k ( k r ωt ) ( k r ω t) v k ( k t) sin r ω ω k v 4//0 PHY 4 A Spring 0 -- Lecture 0

21 B k k Matching electric and magnetic fields at boundary: n n n n + n n k or n n n n + 4//0 PHY 4 A Spring 0 -- Lecture

22 Plane waves reflected and refracted at surface: Matching electric and magnetic fields at boundary: B k k For reflected waves: n n k n n for in plane of incidence + n or for out of plane of incidence: n n n + n n 4//0 PHY 4 A Spring 0 -- Lecture

23 Multiple refractions and reflections in a thin film ( P, t) ± πr sin sin π cos πft ± πr sin ( r + r ) cos π( r r ) av πft sin πft P r r t For n > n ; π sin ( t) + at nt min at nt m ( m + ) 4//0 PHY 4 A Spring 0 -- Lecture 3

24 xample of interference with + n < n < n 3 n For each surface with n < n - for reflected beam n n 3 I I peaks at { ( ( A B) )} cos π m ( A B) π ( r r ) 4//0 PHY 4 A Spring 0 -- Lecture 4

25 xample of interference with n > n n n I I { ( ( A B) )} sin peaks at π( r r ) ( A B) ( m )π + n xample of interference with + I { ( ( A B) )} cos 4//0 PHY 4 A Spring 0 -- Lecture 5 I peaks at π m ( A B) π ( r r )

26 4//0 PHY 4 A Spring 0 -- Lecture 6 Summary 0 0 ima at sin 4 ima at cos 4 n m L I I n m L I I n L L ϕ ϕ π π ϕ + > >

27 xample: Suppose you want to prepare a surface so that it has minimal reflection such as in a solar cell where it is desirable to optimize refraction and minimize reflection at 550nm. n t t ( m + ) ( m + ) ( m + ) SiO n SiO 550 nm nm (for m 0) 4//0 PHY 4 A Spring 0 -- Lecture 7

28 xample: Suppose you see a rainbow pattern for oil on a pavement. What is the the approximate thickness of the oil in the red (700nm) region. Assume that n oil.4. n t t ( m + ) ( m + ) ( m + ) oil n oil 700 nm.4 5 nm, 375 nm, etc. 4//0 PHY 4 A Spring 0 -- Lecture 8