Find the phase difference in terms of d, lambda, theta

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joelkato1605
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Homework Statement
Referring to Figure 4.8, what is the phase difference φ between S¯1 and S¯2 in terms of d,
θ and λ.
Relevant Equations
See attached image.
So in figure 4.8 the path difference between the two waves is d*sin(theta), then is the phase difference just (d*sin(theta)*2*pi)/lambda?
 
Attachments
  • Two-slit interference geometry: slits S1 and S2 separated by d, a dashed line at angle theta to a screen point P at distance x and height y, with the extra path length d sin(theta) marked at S2.
    Capture.PNG
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  • Phasor diagram: red arrow S1 horizontal, red arrow S2 at angle Φ to S1, black arrow S1 + S2 as the resultant. Dashed red lines show S2 cos(Φ) horizontal and S2 sin(Φ) vertical.
    Capture.PNG
    4.7 KB · Views: 203
  • Text page on wave interference from a textbook, giving equations 4.18 and 4.19 for maxima and nulls of two sources, and equations 4.20 and 4.21 for the summed amplitude of two waves.
    Capture.PNG
    40.4 KB · Views: 183
joelkato1605 said:
So in figure 4.8 the path difference between the two waves is d*sin(theta)
This is a good approximation for the path difference when ##d << x##.

then is the phase difference just (d*sin(theta)*2*pi)/lambda?
Yes