Interference and Diffraction of Waves Chapter 28 Interference and Diffraction of Waves

Interference Light waves interfere with each other much like mechanical waves do All interference associated with light waves arises when the electromagnetic fields that constitute the individual waves combine

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

Conditions for Interference For sustained interference between two sources of light to be observed, there are two conditions which must be met The sources must be coherent They must maintain a constant phase with respect to each other The waves must have identical wavelengths

Producing Coherent Sources Light from a monochromatic source is allowed to pass through a narrow slit The light from the single slit is allowed to fall on a screen containing two narrow slits The first slit is needed to insure the light comes from a tiny region of the source which is coherent Old method

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.

Producing Coherent Sources, cont Currently, it is much more common to use a laser as a coherent source The laser produces an intense, coherent, monochromatic beam over a width of several millimeters

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

Let’s see the interference of water ripples. http://www.falstad.com/ripple/

Young’s Double Slit Experiment Thomas Young first demonstrated interference in light waves from two sources in 1801 Light is incident on a screen with a narrow slit, So The light waves emerging from this slit arrive at a second screen that contains two narrow, parallel slits, S1 and S2

Young’s Double Slit Experiment, Diagram The narrow slits, S1 and S2 act as sources of waves The waves emerging from the slits originate from the same wave front and therefore are always in phase

Resulting Interference Pattern The light from the two slits form a visible pattern on a screen The pattern consists of a series of bright and dark parallel bands called fringes Constructive interference occurs where a bright fringe occurs Destructive interference results in a dark fringe

Interference Patterns Constructive interference occurs at the center point The two waves travel the same distance Therefore, they arrive in phase

Interference Patterns, 2 The upper wave has to travel farther than the lower wave The upper wave travels one wavelength farther Therefore, the waves arrive in phase A bright fringe occurs

Interference Patterns, 3 The upper wave travels one-half of a wavelength farther than the lower wave The trough of the bottom wave overlaps the crest of the upper wave This is destructive interference A dark fringe occurs

Young’s Double Slit Experiment (1802)

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

|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

|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 = (2m+1)l/2 (±l/2, ±3l/2,…) Destructive d(x/h) = ml  x = (h/d)ml for constructive int. d h q x 3rd 2nd 1st 0th

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

However, this analysis 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