Physics for Scientists and Engineers
Physics for Scientists and Engineers
6th Edition
ISBN: 9781429281843
Author: Tipler
Publisher: MAC HIGHER
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Chapter 33, Problem 37P

(a)

To determine

The spacing between successive maxima near the center fringe.

(a)

Expert Solution
Check Mark

Explanation of Solution

Given:

The wavelength of the light used is 500nm .

The separation between the slits is 1cm .

The distance between slits and the screen is 1m .

Formula used:

Write the expression for the distance on the screen to the mth bright fringe.

  ym=mλLd   ...... (1)

Here ym is the distance for mth bright fringe, λ is the wavelength of the light used, L is the distance between slits and the screen, d is theseparation between the slits and m is an integer.

Write the expression for the distance on the screen to the (m+1)th bright fringe.

  ym+1=(m+1)λLd   ...... (2)

Here ym+1 is the distance for (m+1)th bright fringe

Subtract equation (2) from equation (1).

  Δy=ym+1ym=(m+1)λLdmλLd=λLd   ...... (3)

Here Δy is the separation between (m+1)th and mth bright fringe.

Calculation:

Substitute 500nm for λ , 1cm for d and 1m for L in equation (3).

  Δy=( 500nm( 10 9 m 1nm )( 1m ) 1cm( 10 2 m 1cm ))=50( 10 6)m=50( 10 6)( μm 10 6 m)m=50μm

Conclusion:

Thus, the spacing between successive maxima near the center fringe is 50μm .

(b)

To determine

The observation of the interference of the light on the screen for the given arrangement.

(b)

Expert Solution
Check Mark

Explanation of Solution

Given:

The wavelength of the light used is 500nm .

The separation between the slits is 1cm .

The distance between slits and the screen is 1m .

Formula used:

Write the expression for the distance on the screen to the mth bright fringe.

  ym=mλLd   ...... (1)

Here ym is the distance for mth bright fringe, λ is the wavelength of the light used, L is the distance between slits and the screen, d is theseparation between the slits and m is an integer.

Write the expression for the distance on the screen to the (m+1)th bright fringe.

  ym+1=(m+1)λLd   ...... (2)

Here ym+1 is the distance for (m+1)th bright fringe

Subtract equation (2) from equation (1).

  Δy=ym+1ym=(m+1)λLdmλLd=λLd   ...... (3)

Here Δy is the separation between (m+1)th and mth bright fringe.

Write the expression for Rayleigh criterion.

  θ=1.22λD   ...... (4)

Here θ is the angle of resolution and D is the diameter of the slit opening.

Calculation:

Substitute 500nm for λ , 1cm for d and 1m for L in equation (3).

  Δy=( 500nm( 10 9 m 1nm )( 1m ) 1cm( 10 2 m 1cm ))=50( 10 6)m=50( 10 6)( μm 10 6 m)m=50μm

For simplicity, take D=Δy

Substitute 50μm for D and 500nm for λ in equation (4).

  θ=1.22( 500nm( 10 9 m 1nm ) 50μm( 10 6 m 1μm ))=1.22100rad=0.0122rad

Conclusion:

Thus, the interference of the light on the screen for the given arrangement will be observed of about 0.0122rad , which is very less.

(c)

To determine

The distance between the slits placed for the maxima.

(c)

Expert Solution
Check Mark

Explanation of Solution

Given:

The wavelength of the light used is 500nm .

The distance between slits and the screen 1m .

The separation between (m+1)th and mth bright fringe is 1mm .

Formula used:

Write the expression for the distance on the screen to the mth bright fringe.

  ym=mλLd   ...... (1)

Here ym is the distance for mth bright fringe, λ is the wavelength of the light used, L is the distance between slits and the screen, d is theseparation between the slits and m is an integer.

Write the expression for the distance on the screen to the (m+1)th bright fringe.

  ym+1=(m+1)λLd   ...... (2)

Here ym+1 is the distance for (m+1)th bright fringe

Subtract equation (2) from equation (1).

  Δy=ym+1ym=(m+1)λLdmλLd=λLd   ...... (3)

Here Δy is the separation between (m+1)th and mth bright fringe.

Simplify the above expression for separation between the slits.

  d=λLΔy   ...... (4)

Calculation:

Substitute 500nm for λ , 1mm for Δy and 1.00m for L in equation (4).

  d=( 500nm( 10 6 mm 1nm )1.00m( 10 3 mm 1m ) 1mm)=0.500mm

Conclusion:

Thus, the distance between the slits is 0.500mm .

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Chapter 33 Solutions

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