Thin Lenses 4/16/2018 1

Transcription

1 Thin Lenses f 4/16/2018 1

2 Thin Lenses: Converging Lens C 2 F 1 F 2 C 1 r 2 f r 1 Parallel rays refract twice Converge at F 2 a distance f from center of lens F 2 is a real focal pt because rays pass through f > 0 for real focal points 1 f (n 1) 1 1 r 1 r 2 n 1 0 because n glass n air r 1 0 because object facing convex surface r 2 0 because object facing concave surface 2

3 Thin Lenses: Diverging Lens f < 0 for virtual focal points C 1 F 2 F 1 C 2 f Extension r 1 r 2 Rays diverge, never pass through a common point F 2 at a distance f F 2 is virtual focal point 3

4 Images from Thin Lenses O C 2 F 1 C 1 I f r 2 r 1 s s 4/16/2018 4

5 Images from Thin Lenses I O F 1 s f s 4/16/2018 5

6 Images from Thin Lenses O C 1 F 2 C 2 s r 1 s r 2 4/16/2018 6

7 Locating Images by Drawing Rays 1 O F F 2 I 1. Ray initially parallel to central axis will pass through F Ray passing through F 1 will emerge parallel to the central axis. 3. Ray passing through center of lens will emerge with no change in direction because the ray encounters the two sides of the lens where they are almost parallel. 4/16/2018 7

8 Locating Images by Drawing Rays 2 I 1 F 2 F 1 O 3 1. Ray initially parallel to central axis will pass through F Backward extension of ray 2 passes through F 1 3. Ray 3 passes through center of lens will emerge with no change in direction. 4/16/2018 8

9 Locating Images by Drawing Rays O 1 F 2 I F Backward extension of ray 1 passes through F 2 2. Extension of ray 2 passes through F 1 3. Ray 3 passes through center of lens will emerge with no change in direction. 4/16/2018 9

10 Two Lens System Note: If image 1 is located beyond lens 2, s 2 for lens 2 is negative. O Lens 1 Lens 2 1. Let s 1 represent distance from object, O, to lens 1. Find s 1 using: 2. Ignore lens 1. Treat Image 1 as O for lens 2. s f s 1 1 s 1 ' f s 2 2 s 2 ' 3. Overall magnification: M m 1 m 2 4/16/ s 1 ' s 1 s 2 ' s 2

11 Example: Two Lens System A seed is placed in front of two thin symmetrical coaxial lenses (lens 1 & lens 2) with focal lengths f 1 =+24 cm & f 2 =+9.0 cm, with a lens separation of L=10.0 cm. The seed is 6.0 cm from lens 1. Where is the image of the seed? Lens 1: 1 f 1 1 s 1 1 s 1 ' s 1 ' 8.0cm Image 1 is virtual. Lens 2: Treat image 1 as O 2 for lens 2. O 2 is outside the focal point of lens 2. So, image 2 will be real & inverted on the other side of lens 2. s 2 L s 1 ' 18cm f 2 s 2 s 2 ' s 2 ' 18.0cm Image 2 is real. 4/16/

12 Example Figure Lens 1 Lens 2 f 1 O f 2 s 1 L 4/16/

13 Table for Lenses Lens Type Object Location Image Location Image Type Image Orientation Sign of f, s, m Converging Inside F Same side as object Virtual Same as object +, -, + Converging Outside F Side of lens opposite the object Real Inverted +, +, - Diverging Anywhere Same side as object Virtual Same as object -, -, + 4/16/

14 LECTURE 26: Interference

15 Interference When two waves with the same frequency f and wavelength combine, the resultant is a wave whose amplitude depends on the phase different,. 4/16/

16 Amplitude (arbitrary units) Amplitude (arbitrary units) Amplitude (arbitrary units) Interference: Phase Differences Constructive Interference = 0 or Position (arbitrary units) Destructive Interference = Position (arbitrary units) = Position (arbitrary units) 4/16/

17 Coherence *If the difference in phase between two (or more) waves remains constant ( i.e., time-independent), the waves are said to be perfectly coherent. *A single light wave is said to be coherent if any two points along the propagation path maintains a constant phase difference. *Coherence length: the spatial extent over which a light wave remains coherent. Only coherent waves can produce interference! 4/16/

18 Coherence Infinite coherence length Finite coherence length Single Photon 4/16/

19 Intensity of Two Interfering Waves *Two light waves not in phase: E E sint 1 o E E sin(t ) 2 o 4/16/

20 Intensity of Two Interfering Waves *Maxima occur for: 2m *Minima occur for: (2m 1) for m = 0, 1, 2, 3. 4/16/

21 Interference *Three ways in which the phase difference between two waves can change: 1. By traveling though media of different indexes of refraction 2. By traveling along paths of different lengths 3. By reflection from a boundary 4/16/

22 Interference: Different Indexes of Refraction *The phase difference between two waves can change if the waves travel through different material having different indexes of refraction. n 1 N 2 N 1 L (n 2 n 1 ) n 2 L 4/16/

23 Interference: Different Path Lengths *The phase difference between two waves can change if the waves travel paths of different lengths. Thomas Young experiment (1801) Remember Huygen s principle. 4/16/

24 Interference: Different Path Lengths *The phase difference between two waves can change if the waves travel paths of different lengths. Interference maxima condition : d sin m m, m 0,1,2,... m order number Interference mimima condition : d sin m m 1, m 1,2, 3,... 2 m order number 4/16/

25 Interference: Different Path Lengths *The phase difference between two waves can change if the waves travel paths of different lengths. d sin Phase difference at a point P: 2 Relationship for distance y from central point to the mth bright fringe on a screen a distance L away: m tan For small angles, tan sin (radians), y m m y L m d m L 4/16/

26 Interference: Different Path Lengths *The phase difference between two waves can change if the waves travel paths of different lengths. Spacing between fringes: y y m1 y m L d 4/16/