Class 12 Physics Wave Optics Youngs double slit experiment

Young’s double slit experiment (YDSE)

The Young’s experiment shows that matter and energy can display both wave and particle characteristics.

Purpose of double slit experiment is as follows:-

1. In order to prove the wave nature of light.
2. To explain the phenomenon of interference.

Two coherent sources of light were taken in order to maintain the 0 or constant phase difference between the sources of light.

• Experimental set-up1:-
• Young took an ordinary source of light(S) such as light bulb.
• The light was made to pass through a very small slit S (which was comparable with the wavelength of light).
• The light coming from Source S was made to pass through two small slits S1 and S2 which were separated by a very small distance d.
• One screen was kept in front of these 2 sources.

Observation1:-

• He observed alternate dark and light bands were formed on the screen.

Setup 2:-

• Now he took 2 light bulbs i.e. 2 non coherent sources of light and placed a screen in front of them.

Observation 2:-

• He observed there were no alternate bands of light formed on the screen.
• Conclusion:-
• When coherent sources of light were taken then the phenomenon of interference is taking place.
• When non-coherent sources were taken phenomenon of interference was not taking place.
• The source S illuminated the sources S1 and S2 as a result the light from S1 and S2 become coherent.
• S was the source of bothS1 and S2, therefore if there is any change in the phase of the source there will be change in the both sources also.
• Therefore both S1 and S2 will be always in phase with each other.

Why alternate sources of light bands were seen

• When the ordinary light source was made to pass through small slit then the wavefront of semicircle shape will be formed.
• Wavefronts are in semicircle shape because of obstacles on both the sides.
• In the figure red bands represents crests and yellow represents troughs.
• When these wavefronts passes through the 2 small slits again the wavefronts will arise.
• There will be points where red and yellow will also overlap with each other.
• Red + Yellow and Yellow + Red à  Destructive interference à Intensity low
• Yellow + Yellow and Red + Red à Constructive interference à Intensity high
• Because of constructive and destructive interference there are alternate dark and light bands seen on the screen.
• Conclusion: -
• When the light wave is originating from the 2 coherent sources they overlap with each other both constructively and destructively.
• As a result alternate light and dark bands of light is shown on the screen.
• This phenomenon of overlapping of light waves giving rise to regions of higher amplitude and regions of lower amplitudeis known as interference.
• Interference is a property related to the wave nature of the light.
• Young’s Double slit experiment proved that the light is of wave nature which was proposed by Huygens principle.

• Important resultsdrawn from the above experiment:-
• Bands were formed as a result of interference and interference was due to the overlapping (either constructive or destructive) of waves.
• Constructive and destructive overlapping depends on the path difference.
• If the path difference is integral multiple of λ = constructive interference.
• If path difference is non integral multiple of λ =destructive interference.

Calculation of path difference

• Let S1 and S2 are the sources and consider a point P where we have to calculate the intensity.
• Path difference = S2P-S1P
• Using Pythagoras theorem :- (S1P) 2 = D2 + (x-(d/2)) 2 equation(1)
• Where D=distance of the screen from 2 slits, x= position of the point where intensity has to be found.
• Similarly (S2P)2 = D2+ (x+(d/2)) 2 equation(2)
• Where d=distance between the 2 small slits.
• Subtracting (2) and (1) => (S2P)2 - (S1P) 2 =(x+(d/2)) 2 - (x-(d/2)) 2
• On simplifying (S2P)2 - (S1P) 2 =2xd
• => (S2P+S1P)(S2P- S1P)=2xd
• =>(S2P- S1P) =(2xd)/(S2P+S1P)
• If d<<D ; x<<D(screen is placed quite far away from the slit arrangement)
• => (S2P+S1P) (are almost same as D).
• => S2P+S1P =2D
• Therefore (S2P- S1P) = (2xd)/(2D)
• Path difference =(xd)/(D)Equation(2)

Observation:-

• Light from coherent sources produced alternate dark and bright bands on the screen placed some distance away from it.

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