Interference (Wavefront)

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!

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. 

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. 

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.