Phy2005 Applied Physics II Spring 2017 Announcements: Exam III April 10 in-class Anne Tolson review Thurs/Fri 5pm? Review Sunday, April 9 4pm NPB 2205 (upstairs) Coverage: Chs. 26-28.1-28.4 NOT 28.5-28.8

Exactly the same as the mirror eq.!!! Now let’s think about the sign. Last time Lens equation and magnification 1/p + 1/q = 1/f M = -q/p Exactly the same as the mirror eq.!!! Now let’s think about the sign. positive negative p real object virtual object (multiple lenses) q real image (opposite side of object) virtual image (same side of object) f for converging lens for diverging lens M erect image inverted image

Last time Nearsighted Farsighted A

(two converging lenses) Last time Compound Microscope (two converging lenses) objective eyepiece po qo pe Magnified inverted virtual image qe Real image formed by the objective lens  an object for the eyepiece lens

Interference and Diffraction of Light Wave Christiaan Huygens (1629 -1695) Thomas Young (1773 -1829) His double slit experiment proved wave-like nature of light.

Interference and Coherent Light Source Any situation in which two or more waves overlap in space Principle of Superposition slinky

Whenever two portions of the same light arrive at the eye by different routes, either exactly or very nearly in the same direction, the light becomes most when the difference of the routes is any multiple of a certain length, and the least intense in the intermediate state of interfering portions; and this length is different for light of different colour. T. Young from a paper to the Royal Society in 1802

Let’s compare interference of light and water waves Veritasium Laser double slit

|r1 – r2| = 0, l, 2l, 3l, …, ml (m: integer)  Constructive Int. • P r1 r2 |r1 – r2| = 0, l, 2l, 3l, …, ml (m: integer)  Constructive Int. |r1 – r2| = l/2, 3l/2, 5l/2, …, (2m+1)l/2  Destructive Int. l

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Q1. Two loudspeakers send out identical sound waves along the x axis. The wavelength of the waves is 70 cm. One speaker is at x=0. A listener is far away. The other speaker starts at x=0 and moved along the x axis to the right. At what 2nd speaker positions between 0<x<2m will the listener hear the loudest sound? (assume both in phase) x 0.35m, 1.05m, 1.75m 0.0m, 0.5m,1.0m,1.5m,2.0m only at 0.0m (4) 0.0m, 0.7m; 1.4m (5) only at 2.0m

|r1 - r2| = dsinq = ml Constructive Int. ● P q s1 s2 d dsinq Along the center line, it is obvious that the distances to two sources are identical.  |r1-r2| = 0 and constructive int. |r1 - r2| = dsinq = ml Constructive Int. = (2m + 1)l/2 Destructive Int. Approximation valid when d << r!!

ml (0, ±l, ±2l, …) Constructive dsinq = (m+1)l/2 (±l/2, ±3l/2,…) Destructive d(x/h) = ml  x = (h/d)ml for constructive int. d h q x 3 2 2nd-order bright fringe 1 1st order bright fringe

d = 0.05 cm h = 100 cm x = 0.36 cm d (x/h) = ml l = (d/m)(x/h) Ex.28.1 In a certain double slit experiment, the slit separation is 0.050 cm. The slit-to-screen distance is 100 cm. When blue light is used, the distance from the central fringe to the fourth-order bright fringe is 0.36 cm. Find the wavelength of the blue light. d = 0.05 cm h = 100 cm x = 0.36 cm m = 4 constructive d (x/h) = ml l = (d/m)(x/h) = (0.05/4)(0.36/100) = 4.5 x 10-5 cm = 450 nm

Note: this analysis is based on the assumptions that the two light sources have exactly the same frequency and they are absolutely in phase all the time. Two identical monochromatic light source: Same frequency and constant phase relation (could be in-phase) Coherent Light Source

Huygen’s principle: Each point on a wavefront acts as a new Coherent light sources by splitting 0th 2nd 1st 3rd Huygen’s principle: Each point on a wavefront acts as a new Source of identical waves.

You can tell when one light beam is a little behind the other, because the pattern shifts! P such a device is an “interferometer”

Interference in thin films Ds = Difference in two routes + = 2x (when qi << 1) Half –reflecting planes 2x = ml constructive = (2m+1)l/2 destructive x x q For an arbitrary angle q Ds = 2x/cosq