Wavelength of visible light under a oil leak

[jarod]

A disabled tanker leaks kerosene (n=1.2) into the Persian Gulf, creating a large slick on the top of water (n=1.3). If you are scuba diving directly under the region of the slick, whose thickness is 460nm, while the Sun is overhead, for which wavelength(s) of visible light is the transmitted intensity strongest?

 

[cristo]

Please show your work before we can help with homework questions

 

[jarod]

This is what i can do:
1) consider this problem as thin-film interference.
2) the strongest intensity occurs at minima dark film in air ( because the observer is diving) ? I cannot explain why!
3) we set up the equation for minima dark film in air: 2L=(m+1/2)\lamda)/1.2
? and put it in the interval from 0.4 to 0.75
4) Solve for lamda.

Any comment?

 

[jarod]

I got the answer 442nm. But somehow, I'm not sure about my steps in the solution. Anyhelp?