Finding (1) wavelength, and (2) thickness of film for constructive interference

[lunaplex]

1) In a double-slit experiment, two parallel slits are illuminated first by light of wavelength 460nm, and then by light of unknown wavelength. The third-order (m = 3) dark fringe resulting from the known wavelength of light falls in the same place on the screen as the second-order (m = 2) bright fringe from the unknown wavelength. What is the unknown wavelength?

2) What is the minimum thickness of a soap bubble needed in order for the reflected light from the outer and inner surfaces to constructively interfere? The light incident on the film has a wavelength of 655nm. Assume that the index of refraction for the soap film is 1.35.

Help would be really appreciated, I've spent over an hour on these two problems and can't figure them out at all.

 

[lanedance]

hi lunaplex - welcome to pf, generally you have a go and get help with your work, rather than someone doing it for you... but here's some hints to get you started

for the first I would revise your double slit notes, probably a useful equation for the intensity based on slit spacing and wavelength floating around - try and understand what it means & how its derived

for the 2nd constructive interfernce in thin films occurs when the reflected light at the top surface is in phase with the light reflected form the bottom surface... have a think how this relates the thickness to the wavelength, remebering some reflections cause phase changes