Destructive Interference of Light Waves in Bubble Film (165 nm)

[stickplot]

Ok so I've been thinking this problem over and over and I understand the problem and its concept but I just don't know where to start and how to do this, someone please guide me through this

Light waves of which wavelength will destructively interfere due to the thickness of the bubble film? The bubble film thickness is 165 nm, with an index of refraction of n = 1.3.

It also contains this picture just showing the different light waves

a= 430 nm
b= 650 nm
c= 860 nm
d= 285 nm

 

[Thaakisfox]

Destructive interference occurs when the phase difference between the two waves is 180 degrees i.e. $$\pi$$

That is, if the two wavelengths are $$\lambda_1\;\;\;,\;\;\; \lambda_2$$, then the condition for destructive interference is:

$$\left|\frac{2\pi}{\lambda_1} nd - \frac{2\pi}{\lambda_2}nd\right|=(2k+1)\pi$$

Where d is the size of the soap film, and n is the refractive index. k is a positive integer.
so from here we have:

$$\left|\frac{1}{\lambda_1}-\frac{1}{\lambda_2}\right|=\frac{2k+1}{2nd}$$

See for which wavelengths this is satisfied, and you are done...

 

[stickplot]

o ok thank you very much i understand it now