Concept explainers
In Figure P27.7 (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?
(a)
The phase difference between waves at pint P when
Answer to Problem 7P
Phase difference is
Explanation of Solution
Write the relation between phase difference and path difference.
Here,
Write the expression for
Here,
Write the expression for
Here,
Rewrite the equation (I) by substituting equation (II).
Conclusion:
Substitute
Thus, the phase difference is
(b)
The phase difference between waves at pint P when
Answer to Problem 7P
The phase difference is
Explanation of Solution
Rewrite equation (I) by substituting equation (III).
Conclusion:
Substitute
Thus, the phase difference is
(c)
The phase difference between waves at point P when
Answer to Problem 7P
The phase difference is
Explanation of Solution
Rewrite equation (IV) in terms of
Conclusion:
Substitute
Thus, the phase difference is
(d)
The value of
Answer to Problem 7P
The value of
Explanation of Solution
Write the relation between path difference and wavelength.
Rewrite the above expression in terms of
Conclusion:
Substitute
Thus, the value of
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