Thin films interference hard problem

[nabilsaleh]

Homework Statement

A 360 nm thick oil film floats on the surface of the water. The indices of refraction of the oil and the water are 1.50 and 1.33, respectively. The surface of the oil is illuminated from above at normal incidence with white light. The two wavelengths of light in the 400 nm to 800 nm wavelength band that are most strongly reflected, in nm, are closest to:

A) 410 and 700
B) 430 and 720
C) 450 and 740
D) 470 and 760
E) 490 and 780

this question came several times on previous exams but i just can't figure out how to solve it and there is no solution online...the answer though is B!

Homework Equations

i'm guessing that i should be using this formula:

2L=((m+1/2)*lamda)/n

lamda is the wavelength
n is the index or refraction

The Attempt at a Solution

 

[ehild]

The formula is all right, just use it. Find the wavelength. You know the layer thickness, the refractive index of oil, and that m is positive integer. Start with m=1.

ehild

 

[nabilsaleh]

The formula is all right, just use it. Find the wavelength. You know the layer thickness, the refractive index of oil, and that m is positive integer. Start with m=1.

ehild

but I have water AND oil ,, I've never done a problem like this ... it's confusing which index to use and when to use it.

 

[nabilsaleh]

The formula is all right, just use it. Find the wavelength. You know the layer thickness, the refractive index of oil, and that m is positive integer. Start with m=1.

ehild

i'm substituting the numbers into the equation but I'm getting results that has nothing to do with the given range :( PLEASE HELP! at least show me how to get one of the wavelengths!

 

[ehild]

One part of the light wave reflects from the upper surface of the oil, other part enters the oil film, reaches the interface with water, and reflects from there. The reflected wave travels through the oil film again, and steps out into air at the front surface. The phase of this wave changes by 4pi n L. It interferes with the directly reflected wave, which suffered a pi phase change upon reflection. The difference between the waves is only that one traveled in oil. You need to use the refractive index of oil and the thickness of the oil film L.

ehild.