Thin Lenses f 1/11/2019

Thin Lenses: Converging Lens f r2 C2 F1 F2 C1 1/s1+n/s’=(n-1)/r1 -n/s’+1/s2=(1-n)/r2 (here r2<0) 1/s1+1/s2=(n-1)(1/r1-1/r2) Parallel rays refract twice Converge at F2 a distance f from center of lens F2 is a real focal pt because rays pass through f > 0 for real focal points

Thin Lenses: Diverging Lens f < 0 for virtual focal points C1 F2 F1 C2 r2 f r1 Extension Rays diverge, never pass through a common point F2 at a distance f F2 is virtual focal point

Images from Thin Lenses C2 F1 C1 O I s’ s 1/11/2019

Images from Thin Lenses 1/11/2019

Images from Thin Lenses C1 F2 C2 r2 s’ r1 O s 1/11/2019

Locating Images by Drawing Rays 1 3 2 F2 F1 O I Ray initially parallel to central axis will pass through F2. Ray passing through F1 will emerge parallel to the central axis. 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. 1/11/2019

Locating Images by Drawing Rays F2 F1 O 2 1 3 I Ray initially parallel to central axis will pass through F2. Backward extension of ray 2 passes through F1 Ray 3 passes through center of lens will emerge with no change in direction. 1/11/2019

Locating Images by Drawing Rays F2 F1 3 I 2 1 O Backward extension of ray 1 passes through F2 Extension of ray 2 passes through F1 Ray 3 passes through center of lens will emerge with no change in direction. 1/11/2019

Two Lens System Lens 1 Lens 2 O s1 Note: If image 1 is located beyond lens 2, s2 for lens 2 is negative. 1. Let s1 represent distance from object, O, to lens 1. Find s1’ using: 2. Ignore lens 1. Treat Image 1 as O for lens 2. 3. Overall magnification: 1/11/2019

Example: Two Lens System A seed is placed in front of two thin symmetrical coaxial lenses (lens 1 & lens 2) with focal lengths f1=+24 cm & f2=+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: Image 1 is virtual. Lens 2: Treat image 1 as O2 for lens 2. O2 is outside the focal point of lens 2. So, image 2 will be real & inverted on the other side of lens 2. Image 2 is real. 1/11/2019

Example Figure Lens 1 Lens 2 O s1 f1 f2 L 1/11/2019

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 +, -, + Outside F Side of lens opposite the object Real Inverted +, +, - Diverging Anywhere -, -, + 1/11/2019

Quiz lecture 25 The radius r in the formula is: Positive Negative 1/11/2019

Quiz lecture 25 The radius r in the formula is: Positive Negative O r 1/11/2019

Quiz lecture 25 The focal length f in the formula is: Positive Negative Positive Negative 1/11/2019

LECTURE 26: Interference http://www.sonic.net/~ideas/graphics/mma_cd.gif Light diffracts…..multiple path lengths ….causes multiple waves to interference producing perfectly destructive interference when it straddles the pit. Wavelength of red light is roughly 700 nanometers http://www.sonic.net/~ideas/graphics/mma_cd.gif http://content.answers.com/main/content/img/CDE/_CDVSDVD.GIF http://electronics.howstuffworks.com/cd1.htm http://content.answers.com/main/content/img/CDE/_CDVSDVD.GIF http://electronics.howstuffworks.com/cd1.htm

Interference When two waves with the same frequency f and wavelength combine, the resultant is a wave whose amplitude depends on the phase different, . Easiest way to achieve the same frequency and wavelength is to use the same source. Lasers are an excellent source of this kind of light. Splitting a laser beam in two beams and making them meet again to combine can result in constructive & destructive interference. 1/11/2019

Interference: Phase Differences  = 0 or 1 Constructive Interference  = 0.5  Destructive Interference  = 0.3  1/11/2019

Coherence Only coherent waves can produce interference! *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. In reality, there are no completely coherent light waves, but partial coherence can be achieved. For instance, sunlight remains coherent only over short distances. *Coherence length: the spatial extent over which a light wave remains coherent. Only coherent waves can produce interference! 1/11/2019

Coherence Single Photon Infinite coherence length If the duration of the E-field oscillation for a photon is one nano-sceond & it travels with the speed of light, the coherence length would be about 30 cm or 1 foot. Coherence length is important because is allows you to determine the length over which interference occurs. 1/11/2019

Intensity of Two Interfering Waves *Two light waves not in phase: 1/11/2019

Intensity of Two Interfering Waves *Maxima occur for: for m = 0, 1, 2, 3…. *Minima occur for: 1/11/2019

Interference *Three ways in which the phase difference between two waves can change: By traveling though media of different indexes of refraction By traveling along paths of different lengths By reflection from a boundary 1/11/2019

Quiz lecture 25 top layer bottom layer ntop = nbottom The light waves of the rays in the figure have the same wavelength and are initially in phase. If 7.60 wavelengths fit within the length of the top layer and 5.50 wavelengths fit within that of the bottom layer, which layer has the greater index of reflection? Top layer top layer bottom layer ntop = nbottom ntop nbottom L 1/11/2019

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. n1 n2 L 1/11/2019

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. 1/11/2019

Interference: Different Path Lengths *The phase difference between two waves can change if the waves travel paths of different lengths. 1/11/2019

Interference: Different Path Lengths *The phase difference between two waves can change if the waves travel paths of different lengths. 1/11/2019

Interference: Different Path Lengths *The phase difference between two waves can change if the waves travel paths of different lengths. Spacing between fringes: 1/11/2019