Thin Film Oil Question

[whitehorsey]

1. A thin film of oil (n_o = 1.50) with varying thickness floats on water (n_w = 1.33). When it is illuminated from above by white light, the reflected colors are as shown in the figure. In air, the wavelength of yellow light is 580 nm.
a. Why are there no reflected colors at point A?
b. What is the oil's thickness t at point B?

3. a. Because it is a destructive interference? the reflected ray from air to oil (phase change) and oil to water (no phase change) so they cancel out?

b. Why is this one a constructive interference? I've read that because there is light it is always constructive but when its dark it is destructive is that true?

 

[ehild]

1. A thin film of oil (n_o = 1.50) with varying thickness floats on water (n_w = 1.33). When it is illuminated from above by white light, the reflected colors are as shown in the figure. In air, the wavelength of yellow light is 580 nm.
a. Why are there no reflected colors at point A?
b. What is the oil's thickness t at point B?

View attachment 61552

3. a. Because it is a destructive interference? the reflected ray from air to oil (phase change) and oil to water (no phase change) so they cancel out?

The ray reflected from the oil-water interface travels across the oil layer and back, and its phase changes during that trip. By how much?

b. Why is this one a constructive interference? I've read that because there is light it is always constructive but when its dark it is destructive is that true?

When two waves interfere the resultant intensity depends on the phase difference between them. How does the phase of a wave of wavelength λ change if it travels D distance?
The interference is destructive if the phase difference between two waves is odd number times pi. It is constructive in case it is integer number times 2pi.

ehild

 

[NascentOxygen]

3. a. Because it is a destructive interference? the reflected ray from air to oil (phase change) and oil to water (no phase change) so they cancel out?

Yes. Though for full marks you'd need to articulate why a "phase change" and why "no phase change".

when its dark it is destructive is that true?

Yes, that explains why the thinnest region is black. Moving to an adjacent slightly less thin region, seen as blue, we can say it remains a region of destructive interference for most wavelengths, but the blue colour indicates that blue is starting to show constructive interference.

 

[whitehorsey]

The ray reflected from the oil-water interface travels across the oil layer and back, and its phase changes during that trip. By how much?

It changes by 180 degrees. So that would cause the rays to cancel out.

Yes. Though for full marks you'd need to articulate why a "phase change" and why "no phase change".

Yes, that explains why the thinnest region is black. Moving to an adjacent slightly less thin region, seen as blue, we can say it remains a region of destructive interference for most wavelengths, but the blue colour indicates that blue is starting to show constructive interference.

Ah okay. But how does the thickness also tell you whether it is constructive or destructive?

 

[ehild]

See http://en.wikipedia.org/wiki/Thin-film_interference

ehild