Concept explainers
(a)
The angles corresponding to the locations of the first three orders of fringes away from the central bright fringe.
(a)
Answer to Problem 76PQ
The angle made by the first bright fringe is
Explanation of Solution
Write the expression for the path difference for bright fringes in Young’s double slit experiment.
Here,
Rearrange the above equation.
Write the expression for the angle made by the first bright fringe from the above equation.
Write the expression for the angle made by the second bright fringe from the equation (II).
Write the expression for the angle made by the third bright fringe from the equation (II).
Conclusion:
Substitute
Substitute
Substitute
Therefore, the angle made by the first bright fringe is
(b)
The distance between the first-order and second order bright fringe.
(b)
Answer to Problem 76PQ
The distance between the first-order and second order bright fringe is
Explanation of Solution
Write the expression for the angle made by a particular interference fringe on the screen from the central maximum.
Here,
Here, for the small angle approximation.
Substitute
Write the expression for the distance between two successive maximum fringes on the screen from the above equation.
Conclusion:
Substitute
Therefore, the distance between the first-order and second order bright fringe is
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