Question on Thin Film Interference

[tigerguy]

Hi - I'm having trouble with the following problem:

A mixture of yellow light (wavelength = 574 nm in vacuum) and violet light (wavelength = 418 nm in vacuum) falls perpendicularly on a film of gasoline that is floating on a puddle of water. For both wavelengths, the refractive index of gasoline is n = 1.40 and that of water is n = 1.33. What is the minimum nonzero thickness of the film in a spot that looks the following colors because of destructive interference, for yellow light?

Because its destructive interference, I'm using the equation t = lambda/2 ,but this is leading to the wrong answer. I'm also making the wavelength for the yellow light equal 410 (574/1.40). Where am I going wrong, or am I even using the right equation? Thanks for your help!

 

[mukundpa]

Do you know about any change in phase of a wave due to reflection.

M.P.

 

[tigerguy]

I think there's a change between the air and oil, but no change between the oil and water? Is that right?

 

[mukundpa]

yes the chang in phase by Pi if the wave is reflected from a denser medium.

 

[tigerguy]

I still don't understand where I'm going wrong. Theres only one phase change, so the value of lambda will change. Then, I divide that value by 2, and I should get my thickness. But, the answer is wrong - why?

I keep on getting 205 nm for the yellow wavelength.

 

[Doc Al]

Your method and answer seem OK to me. Why do you think it's wrong?

 

[tigerguy]

It's an online assignment, and it was marked incorrect - which is why I'm confused.

 

[tigerguy]

Should I maybe try t = lambda x 0.25?
Or, perhaps, my lambda value is incorrect. I'm dividing by 1.40 (to reprsent the gasoline). Is it possible that I should divide by 1.33 first?

I'm feeling really lost on this one, I don't understand why Webassign keeps marking it wrong.

 

[Doc Al]

Should I maybe try t = lambda x 0.25?

If you can afford multiple attempts, I would try that for fun. But that answer is wrong. (But it wouldn't surprise me that they had it backwards.)

Or, perhaps, my lambda value is incorrect. I'm dividing by 1.40 (to reprsent the gasoline). Is it possible that I should divide by 1.33 first?

Nope; that would make no sense.

I'm feeling really lost on this one, I don't understand why Webassign keeps marking it wrong.

It can be picky. Exact format and units might matter. And it's been plain WRONG before.

What was the purpose of giving the information about the violet light? It doesn't enter into the problem. Did you provide the complete statement of the question?

 

[tigerguy]

Hmm - the exact question is:

What is the minimum nonzero thickness of the film in a spot that looks the following colors because of destructive interference?

a. Yellow
b. Violet

I didn't enter it first because I figured the steps for solving both would be the same. Thanks for your help, again.

 

[Doc Al]

Ah... that's much different! If it looks yellow, that means it's the violet light that's destructively interfered! And vice versa.

 

[tigerguy]

Ohhhh I understand now! Thanks!