Atreyi SahaPhysics 132Prof. HatchJanuary 29, 2016Lecture # 5- Homework help: If you have two sources of waves, and the difference is an integer number of path lengths (i.e. 2, 3, 4...wavelengths) then the two waves will be in phase, anexample of constructive interference.. If the difference is a non integer value, more specifically a 1/2 value (i.e. 2.5 wavelengths), then the two waves will be completely out of phase, an example of destructive interference. If the difference is a non integer value, more specifically 1/4 value, then the two waves are beginning to interact destructively. If the difference is a non integer value, more specifically 3/4 value, then the two waves are beginning to interact constructively.- Young's Double Slit Experiment Demoo On the screen, it looks like bright,dark, bright, dark spots alternating.Inside each bright spot, there is a dark spot in there as well There are two types of interferenceo When light goes through one opening that is proportional to the size of the wavelength (the opening is on the order of what a wavelength would be), light goes through and interacts with the two sides of the slits and creates two sources of lights which create two types of interference patterns superimposed on each other. Pattern 1: Light creates a major interference pattern (bright-dark-bright-dark) horizontally. This is from single slit. Pattern 2: Double slit interference is the little horizontal dark-bright spots you see in the middle bright spots unitso Major take home point: light is complicated and when it goes around sharp edges,it creates differentinterference patterns.Corner sharp edges endup acting like differentlight sources.Monochromatic: light that is all the samewavelength & in-phase, light from yourlight bulb is not monochromatic (mix ofdifferent wavelengths)Light goes through two slits whichcreates two light sources/waves and wesee bright and dark spots. Black line: The light is the brightest inthe middle and then it gets darker anddarker as we go out. ; Lightning Bolt: Dark in the middle and then it will get brighter and brighter.Why is this the case?When the two waves interfere perfectly constructively, you get a bright spot. When two waves interfere perfectly destructively, you get a dark spot. However, the two waves won't always interfere perfectly. There will parts of the waves that will be partly in phase or out of phase. For example, when they are a little bit out of phase, the bright spot will be dimmer until itbecomes a dark spot with the two waves interfering perfectly destructively.Problem solving tips: If you see the light, in phase. If you don't see the light, it is out of phase.Distances are uniform: the distance between any two bright spots is the same; the distance between any two dark spots is the same. This is because the wavelengths are uniform - the light is not changing its size as it propagates along. Quantitative AnalysisThe circled area represents the slits, where openings are. The slits are small and the screen is much larger than the separation distance between the two slits. This allows us to make an assumption that the light that leaves from the two slits are effectively parallel to each other. The two sources of lights are parallel (transformed onto B).The circled distance in B is what you need to focus on. This is the extra distance that one of the light waves had to travel. If it the two light waves are parallel, then they have travelled the same distance past the triangle. To calculate the circled distance, use wavelengths.If that little extra distance is one wavelength farther than the other one, at the very end, the waveswill interfere constructively because the difference will be an integer amount. If that little extra distance is half wavelength farther than the other one, at the very end, the waves will interfere destructively because the difference will be a half-integer amount.Won't have to calculate thetaExample problem: Bright spot: we know that the two waves are in phase because there is a bright spot & you will beable to see the light.Q: How many wavelengths of difference is there between the two path lengths?We will use the wavelength of the light as a distance measuring tool because the wavelength is consistent. If I have 100nm light, then I know each wavelength is 100 nm so you can count the number of wavelengths to get a distance. A(?): Zero because they appear to be equal - equal angle and everything. Central one numbered zero because there is no difference in path length.At m = 1, the difference in path length is exactly one wavelength difference. It went from bright to destructive to constructive once again. Bottom wavelength had to travel a greater distance. You can also have 0.5/0.75/decimal differences because dark and bright spots are spread out. Right in the middle is the perfect integer value. Close to in phase =brighter, close to out of phase = darker- Interference Patterns (middle)o The bright spot is in the middle where no light actuallywent through. Light originated at two sources (was split attwo sources) and travelled in a curve pattern until theymet at the bright area. This proves the wave nature of light - there is noway light could be there unless it propagates as awave.o Constructive interference occurs at the center point The two waves travel the same distance andtherefore arrive in phase- Interference Patterns (at the edge)o upper wave has to travel farther than the lower waveo more specifically, the upper wave travels one wavelengthfarther...this is why the waves arrive in phase this creates a bright fringe because the differenceis an integer number and this means constructiveinterference- Interference patterns (destructive)o the upper wave travels 1/2 of a wavelength farther thanthe lower wavelengtho thus, the trough of the wave overlaps the crest of the upper wave resulting in a destructive interference- Equations for the double slit experimento y = defined as the distance from thecentral bright spot to whatever spot youcare about will give you position of the dark or bright fringeo L will be a big number since it is the distance to the screeno d = how far apart the slits are, we do not need to worry about the size of the slitso m is the spot we care about OR the number of gaps to the bright spot dark fringe formula = 1/2 is there because you want to interact destructively- Example problem 1: A pair of narrow slits, separated by 1.8 mm, is
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