Physics thin film interference help

btw the 8 x 10^-7 is supposed to say 3.8 x 10^-7

The pictures a touch too blurry to read.

In any case, for the thin film interference conditions you're looking for, consider the path differences that occur when light passes into the film. The ray that passes into the fat will travel an extra path length with some refractive index n of the fat.

That should help a bit.

Apologies for the blurry photo, hopefully the edited version is a bit better

And thank you for the help! How can you tell by the photo what the path difference will be? (if you can see the photo now😂)

Nichijou-grade gold, I can't! XD

Anyway,

When light travels a distance through a medium (I can count a vacuum as one. There's just nothing there! Though that might not be technically true. Who cares. You get the idea.) it has a path length. The refractive index n multiplied by the distance l equals this path length.

If you can geometrically formulate it, as in your case, and perhaps apply some small angle approximations, you should be able to whip out a length of some sort... I spat some tea while writing that.

Remember the interference conditions too, for constructive/etc, and consider the wavelengths involved.