2. Band Brightness
The next stage in my investigation was to use my theory to quantitatively predict the relative brightness of the bands (areas between rings). As shown in the photo to the left the rings get darker the further from the centre they are.
Using my theory and experimentally determined relationships specific to my setup I predicted the following relationship for the brightness of the nth band with respect to tube dimensions.
- IR is the relative intensity of the nth band (expressed as a proportion of initial intensity)
- DR is the relative intensity due to the path length (this only has a small effect)
- θR is the relative intensity due to reflection off the surface at angle θ and depends on several factors including θ, the surface material and condition, and the colour of light being used. This relationship was determined experimentally for my setup.
- Lis the tube length
- φ is the tube diameter
- n is the number of reflections
I then compared the values predicted by my formula to the measured relative intensity taken from the same photo (the RGB values were calibrated to an actual intensity). The predictions made were very accurate, as can be seen in the graph below.
However it should be noted that the predictions I made were discrete, not continuous as the graph indicates. My method only made predictions for the average intensity of light within each band. The lines on the graph are just trendlines.
One aspect of the phenomenon that was often raised by other teams was the possible role of interference in the patterns formed. Based on my theory I did not believe this had a significant effect. To test this I took photos of the patterns formed by two different lasers. The experiment was to shine a laser at a white board and view the dot through a tube, using the exact same tube and without changing the set up I switched the laser for another with a different wave length. The two lasers used were red (λ = 633 nm) and green (λ = 532 nm). If interference was having an effect on the patterns the two patterns created by the different lasers would be significantly different.
As shown in the photos, the laser ring positions are the same, showing that interference does not play a role in producing the images formed.
Note: The red rings appear brighter than the green due to the difference in sensitivity of the camera to different wavelengths of light. It is interesting to note that when viewed directly the green rings appear brighter as the human eye is more sensitive to green light than red