Why Does a Soap Film of Thickness Lambda/4 Maximize Brightness?

[positron]

There is a soap film of thickness t in air. I don't understand intuitively why a film thickness of of t = lambda/4 where lambda is the length of the light that is incident upon the film, results in maximum brightness of the light. I know that this is true from the equation for interference but I don't understand the equation.


Also, here is another inference problem:
If two wave sources have different wavelengths, what do the nodal and antinodal lines look like? I am thinking that there will still be interference, but the lines will shift. Will they still be lines?

 

[member 553083]

Yes, the interference will still result in nodal and antinodal lines. However, since the two wave sources have different wavelengths, the locations of the nodal and antinodal lines will be different than if they had the same wavelength. Instead of the lines being at regular intervals, the lines will be shifted in a pattern determined by the wavelengths of the two wave sources.