Why do the LINES in a vertical soap bubble get thinner as we go down?

Question

I understand that the soap bubble gets thicker at the bottom of the bubble due to gravity, resulting in a complicated array of different colors of different wavelengths being constructively and destructively interfered in different amounts.

However, as can be seen from the image of a vertical soap bubble, the lines get thinner as we go down. My physics teachers told me that "Although the bands are of equal length initially, after a while you hold the bubble up vertically, as the change in the d (thickness of film) gets LESS as you go down where it is thicker, the bands will also get thinner (think of the bubble as a "vase shape")

Doesn't the change in the thickness of the soap film get more harsher as we go down (since gravity pulls the film layer down)? In addition, if the change in the film layer width gets LESS, shouldn't we see bigger bands resulting from the overall similar pattern of different wavelengths interfering? Or is there a better explanation for why the band lines get thinner as we go down?

Answer 1

You are seeing fringes of equal thickness where light from a source is being reflected off the top of the soap film and the bottom of the soap film and then entering your eye to form an interference pattern on the retina of your eye with your eye focussed on the soap film.

The condition for a maximum is $2 \, n\, t_{\rm m} = (m+\frac 12) \lambda$ where $n$ is the refractive index of water, $t_{\rm m} $ is the thickness of the film, $\lambda$ is the wavelength of light and $m$ is an integer often aclled the order of the interference pattern.

Below there are the three possible vertical sections of the soap film.

You can think of the fringes as contour lines along which the thickness of the soap film is constant.

If the top of the film is at the left and the bottom at the right then the right hand diagram is consistent with your observations.

The thickness of the soap film increases at a faster rate further down the film.

The colouration of the fringes is due the fact that the white light is made up of many wavelengths of light each of which have a distinctive fringe pattern and you are observing the overlap of all such fringe patterns.

As time progresses the film drains and the fringes are seen to move down until in the end the film at the top is so thin, $t < \frac{\lambda}{2n}$, than only distructive interference is possible.