Physics
Physics
5th Edition
ISBN: 9781260486919
Author: GIAMBATTISTA
Publisher: MCG
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Chapter 25, Problem 91P

(a)

To determine

The width of the slits.

(a)

Expert Solution
Check Mark

Answer to Problem 91P

The width of the slits is 0.10mm_.

Explanation of Solution

Write the expression for the width of the central maximum.

    W=2x                                                                                                                     (I)

Here, W is the width of the central maximum, x is the distance between first minimum and the central maximum.

Write the expression for the single-slit diffraction minima.

  asinθ=mλ                                                                                                            (II)

Here, a is the slit width, θ is the angle between the central maximum and first minimum, m is the order of the diffraction, λ is the wavelength of light used.

Equation (II) is used mainly for dark spots on the screen. The width of the central maximum can be quantified as the distance between the minima on each side with m=1,

    asinθ=λ                                                                                                              (III)

Solve equation (III) for a,

    a=λsinθ                                                                                                                (IV)

Since θ is very small, the approximation, sinθtanθ can be used in equation (IV).

    a=λtanθ                                                                                                                (V)

Write the expression for the distance x.

    x=Dtanθ                                                                                                             (VI)

Here, D is the distance between slit and the screen.

Use equation (VI) in (V).

  a=λDx                                                                                                                 (VII)

Conclusion:

Substitute 2.40cm for W in equation (I) and solve for x.

    x=2.40cm2=1.20cm

Substitute 1.20cm for x, 510nm for λ, and 2.4m for D in equation (VII) to find a.

    a=(510nm)(2.4m)1.20cm=(510nm×1m1×109nm)(2.4m)1.20cm×1m100cm=1.02×104m×1000mm1m=0.10mm

Therefore, the width of the slits is 0.10mm_.

(b)

To determine

The distance between slits.

(b)

Expert Solution
Check Mark

Answer to Problem 91P

The distance between slits is 0.51mm_.

Explanation of Solution

Write the expression for the maxima in a double slit interference experiment.

    dsinθ=mλ                                                                                                        (VIII)

Here, d is the distance between the slits.

Rewrite equation (VIII) for fifth order double slit interference experiment,

    dsinθ=5λ                                                                                                          (IX)

Divide equation (IX) and equation (III),

dsinθasinθ=5λλda=5d=5a                                                                                                         (X)

Conclusion:

Substitute 0.10mm for a in equation (X) to find d.

    d=5(0.10mm)=0.51mm

Therefore, the distance between slits is 0.51mm_.

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