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.
The video below gives a short introduction to the concept of Interference, as well as looking at the confusion this can occur!
Young's Double Slit experiment - Advanced Higher
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.
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 :-
NP = S1P
This gives an overall path difference to point P as :-
S2P - S1P = S2N = mλ
As point P is the 1st Order maxima, :-
S2N = 1 x 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 :-
sinθ = ( S2N / S1S2 ) = λ/d
Also looking at the triangle MPO :-
tanθ = OP/MO = Δx/D
But as stated earlier sinθ ~ tanθ ~ θ, therefore :-
Δx = λD/d
The above formula is normally stated in terms of Wavelength :-
λ = Δxd/D
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 ?
λ = Δxd/D
Δx = 1.4 / 10 = 0.14 cm = 1.4x10-3 m
d = 4x10-4 m
D = 1 m
λ = ( 1.4x10-3 x 4x10-4 ) / 1
λ = 5.6x10-7 m
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.
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.