The nth -order differection angle for the shortest wavelength and change in two angles if the distance between the screen and the grating is doubled.

Question

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Answer 1

Question

Chapter 27, Problem 10TP

To determine

The nth -order differection angle for the shortest wavelength and change in two angles if the distance between the screen and the grating is doubled.

Expert Solution & Answer

Answer to Problem 10TP

The nth -order differection angle for the shortest wavelength is 23.578° and change in angle for the longest wavelength and shortest wavelength if the distance between the screen and the grating is doubled is 29.552° and 12.042° respectively.

Explanation of Solution

Given:

The nth -order diffraction angle for the longest wavelength is, θl1=53.13°.

The longest wavelength is, λl=760 nm.

The shortest wavelength is, λs=380 nm.

Formula used:

The wavelength of constructive interference is given by,

λ=dsinθm

The new distance between slits in given by,

d′=2d

The change in angle is given by,

θd=|θ1−θ2|

Calculation:

The distance between slits is calculated as,

d=mλsinθ=n⋅760 nmsin53.13=(760 nm×1.25)n=950n nm

The nth -order differection angle for the shortest wavelength is calculated as,

θs1=sin−1( mλd)=sin−1( n⋅380 nm 950n nm)=23.578°

The new distance between the slits is calculated as,

d′=2d=2×950n nm=1900n nm

The nth -order differection angle for the longest wavelength when d is doubled is calculated as,

θl2=sin−1( mλ d ′)=sin−1( n⋅760 nm 1900n nm)=23.578°

The nth -order differection angle for the shortest wavelength when d is doubled is calculated as,

θs2=sin−1( mλ d ′)=sin−1( n⋅380 nm 1900n nm)=11.536°

The change in angle for longest wavelength is calculated as,

θl=|θl1−θl2|=|53.13°−23.578°|=29.552°

The change in angle for shortest wavelength is calculated as,

θs=|θs1−θs2|=|23.578°−11.536°|=12.042°

Conclusion:

The nth -order differection angle for the shortest wavelength is 23.578° and change in angle for the longest wavelength and shortest wavelength if the distance between the screen and the grating is doubled is 29.552° and 12.042° respectively.

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Answer 2

Question

Chapter 27, Problem 10TP

To determine

The nth -order differection angle for the shortest wavelength and change in two angles if the distance between the screen and the grating is doubled.

Expert Solution & Answer

Answer to Problem 10TP

The nth -order differection angle for the shortest wavelength is 23.578° and change in angle for the longest wavelength and shortest wavelength if the distance between the screen and the grating is doubled is 29.552° and 12.042° respectively.

Explanation of Solution

Given:

The nth -order diffraction angle for the longest wavelength is, θl1=53.13°.

The longest wavelength is, λl=760 nm.

The shortest wavelength is, λs=380 nm.

Formula used:

The wavelength of constructive interference is given by,

λ=dsinθm

The new distance between slits in given by,

d′=2d

The change in angle is given by,

θd=|θ1−θ2|

Calculation:

The distance between slits is calculated as,

d=mλsinθ=n⋅760 nmsin53.13=(760 nm×1.25)n=950n nm

The nth -order differection angle for the shortest wavelength is calculated as,

θs1=sin−1( mλd)=sin−1( n⋅380 nm 950n nm)=23.578°

The new distance between the slits is calculated as,

d′=2d=2×950n nm=1900n nm

The nth -order differection angle for the longest wavelength when d is doubled is calculated as,

θl2=sin−1( mλ d ′)=sin−1( n⋅760 nm 1900n nm)=23.578°

The nth -order differection angle for the shortest wavelength when d is doubled is calculated as,

θs2=sin−1( mλ d ′)=sin−1( n⋅380 nm 1900n nm)=11.536°

The change in angle for longest wavelength is calculated as,

θl=|θl1−θl2|=|53.13°−23.578°|=29.552°

The change in angle for shortest wavelength is calculated as,

θs=|θs1−θs2|=|23.578°−11.536°|=12.042°

Conclusion:

The nth -order differection angle for the shortest wavelength is 23.578° and change in angle for the longest wavelength and shortest wavelength if the distance between the screen and the grating is doubled is 29.552° and 12.042° respectively.

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Answer 3

Question

Chapter 27, Problem 10TP

To determine

The nth -order differection angle for the shortest wavelength and change in two angles if the distance between the screen and the grating is doubled.

Expert Solution & Answer

Answer to Problem 10TP

The nth -order differection angle for the shortest wavelength is 23.578° and change in angle for the longest wavelength and shortest wavelength if the distance between the screen and the grating is doubled is 29.552° and 12.042° respectively.

Explanation of Solution

Given:

The nth -order diffraction angle for the longest wavelength is, θl1=53.13°.

The longest wavelength is, λl=760 nm.

The shortest wavelength is, λs=380 nm.

Formula used:

The wavelength of constructive interference is given by,

λ=dsinθm

The new distance between slits in given by,

d′=2d

The change in angle is given by,

θd=|θ1−θ2|

Calculation:

The distance between slits is calculated as,

d=mλsinθ=n⋅760 nmsin53.13=(760 nm×1.25)n=950n nm

The nth -order differection angle for the shortest wavelength is calculated as,

θs1=sin−1( mλd)=sin−1( n⋅380 nm 950n nm)=23.578°

The new distance between the slits is calculated as,

d′=2d=2×950n nm=1900n nm

The nth -order differection angle for the longest wavelength when d is doubled is calculated as,

θl2=sin−1( mλ d ′)=sin−1( n⋅760 nm 1900n nm)=23.578°

The nth -order differection angle for the shortest wavelength when d is doubled is calculated as,

θs2=sin−1( mλ d ′)=sin−1( n⋅380 nm 1900n nm)=11.536°

The change in angle for longest wavelength is calculated as,

θl=|θl1−θl2|=|53.13°−23.578°|=29.552°

The change in angle for shortest wavelength is calculated as,

θs=|θs1−θs2|=|23.578°−11.536°|=12.042°

Conclusion:

The nth -order differection angle for the shortest wavelength is 23.578° and change in angle for the longest wavelength and shortest wavelength if the distance between the screen and the grating is doubled is 29.552° and 12.042° respectively.

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Answer 4

Question

Chapter 27, Problem 10TP

To determine

The nth -order differection angle for the shortest wavelength and change in two angles if the distance between the screen and the grating is doubled.

Expert Solution & Answer

Answer to Problem 10TP

The nth -order differection angle for the shortest wavelength is 23.578° and change in angle for the longest wavelength and shortest wavelength if the distance between the screen and the grating is doubled is 29.552° and 12.042° respectively.

Explanation of Solution

Given:

The nth -order diffraction angle for the longest wavelength is, θl1=53.13°.

The longest wavelength is, λl=760 nm.

The shortest wavelength is, λs=380 nm.

Formula used:

The wavelength of constructive interference is given by,

λ=dsinθm

The new distance between slits in given by,

d′=2d

The change in angle is given by,

θd=|θ1−θ2|

Calculation:

The distance between slits is calculated as,

d=mλsinθ=n⋅760 nmsin53.13=(760 nm×1.25)n=950n nm

The nth -order differection angle for the shortest wavelength is calculated as,

θs1=sin−1( mλd)=sin−1( n⋅380 nm 950n nm)=23.578°

The new distance between the slits is calculated as,

d′=2d=2×950n nm=1900n nm

The nth -order differection angle for the longest wavelength when d is doubled is calculated as,

θl2=sin−1( mλ d ′)=sin−1( n⋅760 nm 1900n nm)=23.578°

The nth -order differection angle for the shortest wavelength when d is doubled is calculated as,

θs2=sin−1( mλ d ′)=sin−1( n⋅380 nm 1900n nm)=11.536°

The change in angle for longest wavelength is calculated as,

θl=|θl1−θl2|=|53.13°−23.578°|=29.552°

The change in angle for shortest wavelength is calculated as,

θs=|θs1−θs2|=|23.578°−11.536°|=12.042°

Conclusion:

The nth -order differection angle for the shortest wavelength is 23.578° and change in angle for the longest wavelength and shortest wavelength if the distance between the screen and the grating is doubled is 29.552° and 12.042° respectively.

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Answer 5

Chapter 27, Problem 10TP

To determine

The nth -order differection angle for the shortest wavelength and change in two angles if the distance between the screen and the grating is doubled.

Expert Solution & Answer

Answer to Problem 10TP

The nth -order differection angle for the shortest wavelength is 23.578° and change in angle for the longest wavelength and shortest wavelength if the distance between the screen and the grating is doubled is 29.552° and 12.042° respectively.

Explanation of Solution

Given:

The nth -order diffraction angle for the longest wavelength is, θl1=53.13°.

The longest wavelength is, λl=760 nm.

The shortest wavelength is, λs=380 nm.

Formula used:

The wavelength of constructive interference is given by,

λ=dsinθm

The new distance between slits in given by,

d′=2d

The change in angle is given by,

θd=|θ1−θ2|

Calculation:

The distance between slits is calculated as,

d=mλsinθ=n⋅760 nmsin53.13=(760 nm×1.25)n=950n nm

The nth -order differection angle for the shortest wavelength is calculated as,

θs1=sin−1( mλd)=sin−1( n⋅380 nm 950n nm)=23.578°

The new distance between the slits is calculated as,

d′=2d=2×950n nm=1900n nm

The nth -order differection angle for the longest wavelength when d is doubled is calculated as,

θl2=sin−1( mλ d ′)=sin−1( n⋅760 nm 1900n nm)=23.578°

The nth -order differection angle for the shortest wavelength when d is doubled is calculated as,

θs2=sin−1( mλ d ′)=sin−1( n⋅380 nm 1900n nm)=11.536°

The change in angle for longest wavelength is calculated as,

θl=|θl1−θl2|=|53.13°−23.578°|=29.552°

The change in angle for shortest wavelength is calculated as,

θs=|θs1−θs2|=|23.578°−11.536°|=12.042°

Conclusion:

The nth -order differection angle for the shortest wavelength is 23.578° and change in angle for the longest wavelength and shortest wavelength if the distance between the screen and the grating is doubled is 29.552° and 12.042° respectively.

Answer 6

Chapter 27, Problem 10TP

To determine

The nth -order differection angle for the shortest wavelength and change in two angles if the distance between the screen and the grating is doubled.

Expert Solution & Answer

Answer to Problem 10TP

The nth -order differection angle for the shortest wavelength is 23.578° and change in angle for the longest wavelength and shortest wavelength if the distance between the screen and the grating is doubled is 29.552° and 12.042° respectively.

Explanation of Solution

Given:

The nth -order diffraction angle for the longest wavelength is, θl1=53.13°.

The longest wavelength is, λl=760 nm.

The shortest wavelength is, λs=380 nm.

Formula used:

The wavelength of constructive interference is given by,

λ=dsinθm

The new distance between slits in given by,

d′=2d

The change in angle is given by,

θd=|θ1−θ2|

Calculation:

The distance between slits is calculated as,

d=mλsinθ=n⋅760 nmsin53.13=(760 nm×1.25)n=950n nm

The nth -order differection angle for the shortest wavelength is calculated as,

θs1=sin−1( mλd)=sin−1( n⋅380 nm 950n nm)=23.578°

The new distance between the slits is calculated as,

d′=2d=2×950n nm=1900n nm

The nth -order differection angle for the longest wavelength when d is doubled is calculated as,

θl2=sin−1( mλ d ′)=sin−1( n⋅760 nm 1900n nm)=23.578°

The nth -order differection angle for the shortest wavelength when d is doubled is calculated as,

θs2=sin−1( mλ d ′)=sin−1( n⋅380 nm 1900n nm)=11.536°

The change in angle for longest wavelength is calculated as,

θl=|θl1−θl2|=|53.13°−23.578°|=29.552°

The change in angle for shortest wavelength is calculated as,

θs=|θs1−θs2|=|23.578°−11.536°|=12.042°

Conclusion:

The nth -order differection angle for the shortest wavelength is 23.578° and change in angle for the longest wavelength and shortest wavelength if the distance between the screen and the grating is doubled is 29.552° and 12.042° respectively.

Answer 7

Chapter 27, Problem 10TP

To determine

The nth -order differection angle for the shortest wavelength and change in two angles if the distance between the screen and the grating is doubled.

Answer 8

Expert Solution & Answer

Answer to Problem 10TP

The nth -order differection angle for the shortest wavelength is 23.578° and change in angle for the longest wavelength and shortest wavelength if the distance between the screen and the grating is doubled is 29.552° and 12.042° respectively.

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

Explanation of Solution

Given:

The nth -order diffraction angle for the longest wavelength is, θl1=53.13°.

The longest wavelength is, λl=760 nm.

The shortest wavelength is, λs=380 nm.

Formula used:

The wavelength of constructive interference is given by,

λ=dsinθm

The new distance between slits in given by,

d′=2d

The change in angle is given by,

θd=|θ1−θ2|

Calculation:

The distance between slits is calculated as,

d=mλsinθ=n⋅760 nmsin53.13=(760 nm×1.25)n=950n nm

The nth -order differection angle for the shortest wavelength is calculated as,

θs1=sin−1( mλd)=sin−1( n⋅380 nm 950n nm)=23.578°

The new distance between the slits is calculated as,

d′=2d=2×950n nm=1900n nm

The nth -order differection angle for the longest wavelength when d is doubled is calculated as,

θl2=sin−1( mλ d ′)=sin−1( n⋅760 nm 1900n nm)=23.578°

The nth -order differection angle for the shortest wavelength when d is doubled is calculated as,

θs2=sin−1( mλ d ′)=sin−1( n⋅380 nm 1900n nm)=11.536°

The change in angle for longest wavelength is calculated as,

θl=|θl1−θl2|=|53.13°−23.578°|=29.552°

The change in angle for shortest wavelength is calculated as,

θs=|θs1−θs2|=|23.578°−11.536°|=12.042°

Conclusion:

The nth -order differection angle for the shortest wavelength is 23.578° and change in angle for the longest wavelength and shortest wavelength if the distance between the screen and the grating is doubled is 29.552° and 12.042° respectively.