Interference (Wavefront)
Young's Slits Experiment - Higher Recap
Young's Slits Experiment - Higher Recap
In 1801, Thomas Young performed a series of experiments, designed to prove that light was a wave. These experiments form the basis of our understanding of the wave nature of light, and Interference patterns. In order to produce coherent waves Young scored two fine lines, slits, on a blackened plate of glass. Light from a single source could then split into 2 coherent ‘point’ sources by diffraction.
In 1801, Thomas Young performed a series of experiments, designed to prove that light was a wave. These experiments form the basis of our understanding of the wave nature of light, and Interference patterns. In order to produce coherent waves Young scored two fine lines, slits, on a blackened plate of glass. Light from a single source could then split into 2 coherent ‘point’ sources by diffraction.
The video below gives a short introduction to the concept of Interference, as well as looking at the confusion this can occur!
The video below gives a short introduction to the concept of Interference, as well as looking at the confusion this can occur!
Non Examinable Derivation - Young's Double Slit experiment
Non Examinable Derivation - Young's Double Slit experiment
The diagram above shows a single source of monochromatic light incident upon two slits ( S1 and S2 ). As the wave-front reaches the slits, each slit will act a secondary source, dividing the wave-front into two separate waves.
The diagram above shows a single source of monochromatic light incident upon two slits ( S1 and S2 ). As the wave-front reaches the slits, each slit will act a secondary source, dividing the wave-front into two separate waves.
Note - In order to perform the below derivation, it is assumed that D >> d. This allows the approximation of sin θ = tan θ = θ to be used.
Note - In order to perform the below derivation, it is assumed that D >> d. This allows the approximation of sin θ = tan θ = θ to be used.
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In the above diagram, the 1st Order maxima is found at point P.
In the above diagram, the 1st Order maxima is found at point P.
N is a point on the diagram such that the length NP is given by the following :-
N is a point on the diagram such that the length NP is given by the following :-
NP = S1P
NP = S1P
This gives an overall path difference to point P as :-
This gives an overall path difference to point P as :-
S2P - S1P = S2N = mλ
S2P - S1P = S2N = mλ
As point P is the 1st Order maxima, :-
As point P is the 1st Order maxima, :-
S2N = 1 x λ
S2N = 1 x λ
S2N = λ
S2N = λ
As the line PM >> S1S2, the line S1N crosses S2P at ( approximately ) a right angle and S1S2N is a right angled triangle. For this triangle :-
As the line PM >> S1S2, the line S1N crosses S2P at ( approximately ) a right angle and S1S2N is a right angled triangle. For this triangle :-
sinθ = ( S2N / S1S2 ) = λ/d
sinθ = ( S2N / S1S2 ) = λ/d
Also looking at the triangle MPO :-
Also looking at the triangle MPO :-
tanθ = OP/MO = Δx/D
tanθ = OP/MO = Δx/D
But as stated earlier sinθ ~ tanθ ~ θ, therefore :-
But as stated earlier sinθ ~ tanθ ~ θ, therefore :-
Δx = λD/d
Δx = λD/d
The above formula is normally stated in terms of Wavelength :-
The above formula is normally stated in terms of Wavelength :-
λ = Δxd/D
λ = Δxd/D
Example 1 -
Example 1 -
A Young's Slit experiment is set up with a slit separation of 0.4 mm. The fringes are observed on a screen placed 1 m from the slits. If the separation between bright fringes m = 0 and m = 10 is 1.4 cm, what is the Wavelength ( and approximate colour ) of the light used ?
A Young's Slit experiment is set up with a slit separation of 0.4 mm. The fringes are observed on a screen placed 1 m from the slits. If the separation between bright fringes m = 0 and m = 10 is 1.4 cm, what is the Wavelength ( and approximate colour ) of the light used ?
λ = Δxd/D
λ = Δxd/D
Δx = 1.4 / 10 = 0.14 cm = 1.4x10-3 m
Δx = 1.4 / 10 = 0.14 cm = 1.4x10-3 m
d = 4x10-4 m
d = 4x10-4 m
D = 1 m
D = 1 m
λ = ( 1.4x10-3 x 4x10-4 ) / 1
λ = ( 1.4x10-3 x 4x10-4 ) / 1
λ = 5.6x10-7 m
λ = 5.6x10-7 m
λ = 560 nm ( approximately Green / Yellow )
λ = 560 nm ( approximately Green / Yellow )
The above diagram shows the interference patterns generated by monochromatic green light and white light using Young's Slits.
The above diagram shows the interference patterns generated by monochromatic green light and white light using Young's Slits.
Note - As fringe spacing is dependent on Wavelength each bright fringe will show a coloured spectrum ( with red light deviated the most ) and a white central maximum.
Note - As fringe spacing is dependent on Wavelength each bright fringe will show a coloured spectrum ( with red light deviated the most ) and a white central maximum.