Which of the following statements accurately describe reflection interference fo

Question

Which of the following statements accurately describe reflection interference for a thin film where light passes from air into a material with higher index of refraction and then back into air? Some calculation may be useful. (Check all that applied)

A. If constructive interference is not occurring for a particular wavelength, that wavelength must be canceled by destructive interference

B. Various wavelengths of light will constructively interfere in a thin film of increasing thickness before they destructively interfere

C. For a film with increasing thickness, constructive interference begins with short wavelengths of light and moves to longer wavelengths

D. The m = 0 condition for destructive interference is true when the thin film is one wavelength thick

E. The m = 0 condition for constructive interference is true when the film thickness approaches 0

Explanation / Answer

Hi,

In this case, I would say that the statement that is right is the first one, because if no constructive interference is occurring, the interference should be destructive; the occurrence of one excludes the other and vice versa.

Besides, when one is dealing with thin film layers, usually one works with a single wavelength.

In the case of the other ones we have the following:

B. As it was said before, an interference can only be of one of the two types (constructive or destructive). Therefore, if the wavelengths are contructively interfering with each other they shound't destructively interfer all of the sudden.

C. The wavelenght and the thickness are related (somehow) for the following relations:

2nt = (m + 1/2) (constructive interference) ; 2nt = m (destructive interference)

t = thickness, = wavelength ; n = index of refraction.

As we can see, in both cases the thickness of the film is proportional to the wavelength, so we cannot say that because the thickness of the film is increasing (and, therefore, so does the wavelength), the interference will always be constructive.

D. For the destructive interference, the condition m = 0 is reached when the thickness is almost zero.

E. For the constructive interference, the condition m = 0 is reached when the thickness is approximately /4n.

Note: the equations shown here are simplifications of the more complex equations that are used to calculate said parameters, but they served our purpose in this case.

I hope it helps.

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