Thin Lenses f 4/16/2018 1
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
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
Images from Thin Lenses O C 2 F 1 C 1 I f r 2 r 1 s s 4/16/2018 4
Images from Thin Lenses I O F 1 s f s 4/16/2018 5
Images from Thin Lenses O C 1 F 2 C 2 s r 1 s r 2 4/16/2018 6
Locating Images by Drawing Rays 1 O F 1 3 2 F 2 I 1. Ray initially parallel to central axis will pass through F 2. 2. 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
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 2. 2. 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
Locating Images by Drawing Rays O 1 F 2 I F 1 2 3 1. 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
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 1 1 1 1 f s 1 1 s 1 ' 1 1 1 f s 2 2 s 2 ' 3. Overall magnification: M m 1 m 2 4/16/2018 10 s 1 ' s 1 s 2 ' s 2
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 1 1 1 f 2 s 2 s 2 ' s 2 ' 18.0cm Image 2 is real. 4/16/2018 11
Example Figure Lens 1 Lens 2 f 1 O f 2 s 1 L 4/16/2018 12
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 -, -, + 4/16/2018 13
LECTURE 26: Interference http://electronics.howstuffworks.com/cd1.htm http://www.sonic.net/~ideas/graphics/mma_cd.gif http://content.answers.com/main/content/img/cde/_cdvsdvd.gif
Interference When two waves with the same frequency f and wavelength combine, the resultant is a wave whose amplitude depends on the phase different,. 4/16/2018 18
Amplitude (arbitrary units) Amplitude (arbitrary units) Amplitude (arbitrary units) Interference: Phase Differences Constructive Interference 4 3 2 1 0-1 -2-3 = 0 or 1-4 0 20 40 60 80 100 Position (arbitrary units) Destructive Interference 2 1.5 1 0.5 0 = 0.5-0.5-1 -1.5-2 0 20 40 60 80 100 Position (arbitrary units) 3 2 1 0-1 -2 = 0.3-3 0 20 40 60 80 100 Position (arbitrary units) 4/16/2018 19
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! 4/16/2018 20
Coherence Infinite coherence length Finite coherence length Single Photon 4/16/2018 21
Intensity of Two Interfering Waves *Two light waves not in phase: E E sint 1 o E E sin(t ) 2 o 4/16/2018 22
Intensity of Two Interfering Waves *Maxima occur for: 2m *Minima occur for: (2m 1) for m = 0, 1, 2, 3. 4/16/2018 23
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 4/16/2018 24
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 4/16/2018 26
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. 4/16/2018 27
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 4/16/2018 28
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 4/16/2018 29
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 4/16/2018 30