Concept explainers
In Figure P36.10 (not to scale), let L = 1.20 m and d = 0.120 mm and assume the slit system is illuminated with monochromatic 500-nm light. Calculate the phase difference between the two wave fronts arriving at P when (a) θ = 0.500° and (b) y = 5.00 mm. (c) What is the value of θ for which the phase difference is 0.333 rad? (d) What is the value of θ for which the path difference is λ/4?
Figure P36.10
(a)
Answer to Problem 10P
Explanation of Solution
Given info: The separation between the slits is
The given diagram is shown below.
Figure 1
The formula to calculate the phase difference is,
Here,
Substitute
Conclusion:
Therefore, the phase difference between the two waves fronts arriving at
(b)
Answer to Problem 10P
Explanation of Solution
Given info: The separation between the slits is
The formula to calculate the phase difference is,
Here,
From the right angle triangle
Here,
Substitute
Substitute
Conclusion:
Therefore, the phase difference between the two waves fronts arriving at
(c)
Answer to Problem 10P
Explanation of Solution
Given info: The separation between the slits is
The formula to calculate the phase difference is,
Here,
Rearrange the above formula to find
Substitute
Conclusion:
Therefore, the value of
(d)
Answer to Problem 10P
Explanation of Solution
Given info: The separation between the slits is
The formula to calculate the phase difference is,
Here,
The path difference is
Substitute
Rearrange the equation (1) to find
Substitute
Conclusion:
Therefore, the value of
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