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 79PQ

(a)

To determine

The angular separation between the central maximum and an adjacent maximum.

(a)

Expert Solution
Check Mark

Answer to Problem 79PQ

The angular separation between the central maximum and an adjacent maximum is 29.2°.

Explanation of Solution

Write the expression for the speed of the wave.

    v=fλ                                                                                                                 (I)

Here, v is the speed of the wave, λ is the wavelength of the wave and f is the frequency of the wave.

Rearrange the above equation.

  λ=vf                                                                                                                 (II)

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

    dsinθn=nλ                                                                                                     (III)

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)                                                                                        (IV)

Write the expression for the angle made by the central maximum (n=0) from the above equation.

    θ0=sin1(0λd)θ0=0°

Write the expression for the angle made by the adjacent maximum next to the central maximum (n=1) from the equation-(IV).

    θ1=sin1(λd)

Write the expression for the angular separation between the central maximum and an adjacent maximum.

    Δθ=θ1θ0

Substitute sin1(λd) for θ1 and 0° for θ0 in the above equation.

    Δθ=sin1(λd)                                                                                                         (V)

Conclusion:

Substitute 343m/s for v and 1850Hz for f in the equation (II) to find λ.

  λ=343m/s1850Hz=0.1854m

Substitute 38.0cm for d and 0.1854m for λ in the equation (V) to find Δθ.

  Δθ=sin1[0.1854m38.0cm(102m1cm)]=29.2°

Therefore, the angular separation between the central maximum and an adjacent maximum is 29.2°.

(b)

To determine

The separation between the slits for the same angular separation between the central maximum and an adjacent maximum.

(b)

Expert Solution
Check Mark

Answer to Problem 79PQ

The separation between the slits is 5.43×102m.

Explanation of Solution

Write the expression for the separation between the slits from equation-(V).

    Δθ=sin1(λd)sinΔθ=λdd=λsinΔθ                                                                                            (VI)

Conclusion:

Substitute 2.65cm for λ and 29.2° for Δθ in the above equation to find d.

    d=2.65cm(102m1cm)sin29.2=5.43×102m

Therefore, the separation between the slits is 5.43×102m.

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Chapter 35 Solutions

Physics for Scientists and Engineers: Foundations and Connections

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