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:-
- In order to prove the wave nature of light.
- 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.
- He observed alternate dark and light bands were formed on the screen.
- Now he took 2 light bulbs i.e. 2 non coherent sources of light and placed a screen in front of them.
- He observed there were no alternate bands of light formed on the screen.
- 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)
- Light from coherent sources produced alternate dark and bright bands on the screen placed some distance away from it.