I know this questions has many parts but I really want someone to explain and to
ID: 2140484 • Letter: I
Question
I know this questions has many parts but I really want someone to explain and to work out this promblems in detail to fully understant the concepts. I will give many points since I know this is not such an easy task, at least for me its not. Thank so much for your help if you help me I would really appriciate it.
The diagram at right shows an arbitrary point, point A, that lies near two point sources of waves. In this problem, we consider how the path length difference to point A changes as point A is moved along the dark line shown, away from the sources. Point Z on the diagram below was chosen so that point Z and source 5, are equidistant from point A. How do the angles a and beta compare? Explain Suppose that point A is moved away from the sources along the dark line. In the limit that point A it very far from the sources, what values do the angles a.beta, and y approach? On the diagram above, indicate the line segment that represents how much farther point A is from s1 than it is from S2. Label this distance delta D The enlarged diagram at right illustrates the limit in which point A is moved very far from the sources. In this limit, find an expression for delta D in terms of the angle theta and the source separation d (Hint: How do the angles and theta compare?) For what values of thetaD (in terms of lambda) will there be: maximum constructive interference? complete destructive interference (i.e. a node)? Use your answers from parts d and e to write equations that can be used to determine the angle (s) for which there will be: lines of maximum constructive interference nodal lines Determine the angles for which there will be nodal lines and lines of maximum constructive interference for the case of two sources in phase, a distance 1.5 lambda apart Use your results to draw accurate nodal lines and lines of maximum constructive interference on the diagram at right. Label each line from part i with the corresponding value of delta D and theta. If the distance between the sources were increased, would the angle theta to the first nodal line increase, decrease, or stay the same? Explain your reasoning. Consider the following incorrect statement referring to problem 3: "As point A moves farther ond farther away from the sources, the distances to the sources become more nearty equal, so the difference in distances is negligible Thus the waves are more nearly in phase as point A moves farther and farther away from the sources " What is the flaw in this argument? Explain your reasoningExplanation / Answer
3)
a) alfa and beta are same
b) alfa = beta = 90 degrees and gamma = 0
c) delta D = distance from s1 to point Z
d) theta + 90 - alfa = 90
==> theta = alfa
fro figure
cos(90-theta) = S1Z/d
sin(theta) = S1Z/d
==> S1Z = delta D = d*sin(theta)
e) if delta D = m*lamda (m = 0,1,2,3,...)
constructive interference takes place and we get maxima
if delta D = (m + 1/2)*lamda (m = 0,1,2,3,...)
distructive interference takes place and we get minima
f)
for maxima d*sin(theta) = m*lamda (m = 0,1,2,3,...)
for minima d*sin(theta) = (m + 1/2)*lamda (m = 0,1,2,3,...)
g)
4)
even the point A moves further always there is a path difference
between the two waves is d*sin(theta).
so, what ever may be the distnace of point A
the path difference always d*sin(theta)