TOPIC: Interference and Diffraction

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ACTIVITY 1

Using Venn Diagram, give the similarities and differences between interference and diffraction. INTERFERENCE DIFFRACTIONIn your own words, describe the following: Interference DiffractionHuygens's principle: Huygens's principle states that if the position of a wave front at one instant is known, then the position of the front at a later time can be constructed by imagining the front as a source of secondary wavelets. Secondary waveleis 1.1 Applying Huygens's principle to wave front AA' to construct a new wave front BB' Figure 1.1 illustrates Huygens's principle. The original wave front AA' is traveling outward from a source, as indicated by the arrows. We want to find the shape of the wave front after a time interval t. We assume that v, the speed of propagation of the wave, is the same at all points. Then in time t the wave front travels a distance ut. We construct several circles (traces of spherical wavelets) with radius r = ut, centered at points along AA'. The trace of the envelope of these wavelets, which is the new wave front, is the curve BB'.Huygens's principle can be used to derive the laws of reflection and refraction. Law of Reflection - the angles of Or = 0a incidence and reflection are equal. Law of Refraction - relates the angles of incidence and refraction to the n,sinda = nosine. indexes of refraction of the materials. Interference refers to when two or more waves pass through the same region at the same time. When this occurs, the total wave at any point at any instant of time is governed by the principle of superposition. This principle also applies to the electromagnetic waves and is the most important principle in all physical optics. The principle states: When two or more waves overlap, the resultant displacement at any point and at any instant is found by adding the instantaneous displacements that would be produced at the point by the individual waves if each were present alone. There are two types of interference: Constructive and Destructive. Constructive Interference is a type of interference that occurs when the two wave 1 interfering waves have a displacement in AAA the same direction, therefore, they are "in-phase" and will combine together and will increase the amplitude. Constructive Interference wave 1 + wave 2 dsine = mA (m=0, +1, +2, +3 . . .) AAADestructive Interference is a type of interference that occurs when the two interfering waves are "out-of-phase" and they will neglect each other. Destructive Interference wave 2 dsine = (m+1/2)1 (m=0, +1, +2, +3 . . .) where: d = Distance between slits wave 1 + wave 2 0 = Angle of line from slit to mth region (bright/dark) on screen A = Wavelength Note: When 0 is very small, the position ym of Constructive Interference the mth bright fringe on a screen located a (for small angles only) distance R from the sources is given by: ym = R (m=0, +1, 12, 13 . . where: ym = Position of mth bright band A = Wavelength d = Distance between slits R = Distance from slits to screen Intensity in Interference Pattern When two sinusoidal waves with equal amplitude E and phase difference 0 are superimposed, the resultant Ep and intensity I are: Amplitude in Two-Source Interference Ep = 2E | cos (/2) | Intensity in Two-Source Interference I = locos2 ($/2)If the two source emits in phase, the phase difference + at point P (located at distance ri from source 1 and distance ra from source 2) is directly proportional to the path difference r1 - r2: Phase Difference in Two-Source Interference = (2n/A) (r1 - r2) = k(r1 - r2) Phasors rotate counterclockwise. Ep E TT E T wt O E2 = E cos wt E1 = Ecos (wt + p)Two - Slit Experiment- is a demonstration that the light and matter can display characteristics of both classically defined waves and particles. (a). Young's experiment to show Treeis from Payshis interference of light passing through two slits. A pattern of bright and dark areas appears on the screen. kunstindy (b) Geometrical analysis of Young's experiment. For the case shown, r2 > rl and both y and 0 are positive. If point Pis on the other side of the screen's center, 12