Physics for Scientists and Engineers: Foundations and Connections
Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN: 9781133939146
Author: Katz, Debora M.
Publisher: Cengage Learning
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Chapter 35, Problem 76PQ

(a)

To determine

The angles corresponding to the locations of the first three orders of fringes away from the central bright fringe.

(a)

Expert Solution
Check Mark

Answer to Problem 76PQ

The angle made by the first bright fringe is 0.090°. The angle made by the second bright fringe is 0.180°. The angle made by the third bright fringe is 0.270°.

Explanation of Solution

Write the expression for the path difference for bright fringes in Young’s double slit experiment.

    dsinθn=nλ                                                                             (I)

Here, λ is the wavelength of light, d is the separation between two slit, θ is the angle of diffraction and n is an integer.

Rearrange the above equation.

  dsinθn=nλsinθn=nλdθn=sin1(nλd)                                                                (II)

Write the expression for the angle made by the first bright fringe from the above equation.

    θ1=sin1(1λd)                                                                          (III)

Write the expression for the angle made by the second bright fringe from the equation (II).

    θ2=sin1(2λd)                                                                         (IV)

Write the expression for the angle made by the third bright fringe from the equation (II).

    θ3=sin1(3λd)                                                                        (V)

Conclusion:

Substitute 0.350mm for d and 550nm for λ in the equation (III) to find θ1.

  θ1=sin1[1×550nm×(109m1nm)0.350mm×(103m1mm)]=0.090°

Substitute 0.350mm for d and 550nm for λ in the equation (IV) to find θ2.

  θ2=sin1[2×550nm×(109m1nm)0.350mm×(103m1mm)]=0.180°

Substitute 0.350mm for d and 550nm for λ in the equation-(V) to find θ3.

  θ3=sin1[3×550nm×(109m1nm)0.350mm×(103m1mm)]=0.270°

Therefore, the angle made by the first bright fringe is 0.090°. The angle made by the second bright fringe is 0.180°. The angle made by the third bright fringe is 0.270°.

(b)

To determine

The distance between the first-order and second order bright fringe.

(b)

Expert Solution
Check Mark

Answer to Problem 76PQ

The distance between the first-order and second order bright fringe is 3.14×103m.

Explanation of Solution

Write the expression for the angle made by a particular interference fringe on the screen from the central maximum.

    tanθn=ynx

Here, yn is the distance of the particular fringe from the central maximum on the screen and x is the distance between slit and the screen.

Here, for the small angle approximation.

    tanθsinθ

Substitute nλd for tanθ in the above equation to find the expression for yn.

    nλd=ynxyn=nλxd                                                                                (VI)

Write the expression for the distance between two successive maximum fringes on the screen from the above equation.

    Δy=yn+1yn=(n+1)λxdnλxd=λxd                                                             (VII)

Conclusion:

Substitute 0.350mm for d, 2.00m for x and 550nm for λ in the equation (IV) to find Δy.

  Δy=550nm×(109m1nm)×2.00m0.350mm×(103m1mm)=3.14×103m

Therefore, the distance between the first-order and second order bright fringe is 3.14×103m.

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Chapter 35 Solutions

Physics for Scientists and Engineers: Foundations and Connections

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