A thin film of acetone (n = 1.25) coats a thick glass plate (n=1.50). White ligh

Question

A thin film of acetone (n = 1.25) coats a thick glass plate (n=1.50). White light is incident normal to the film. In the reflections, fully destructive interference occurs at 550 nm and fully constructive interference at 596 nm. Calculate the thickness of the acetone film.

Explanation / Answer

Ok we will use the equation for thin-film interference 4d(pi) / (wavelength) + pi - pi = (even Integer) (pi) the + pi is added is due to the phase change from the air to the film while the - pi is due to the phase change from the film to the glass On the right hand side, the even integer corresponds to constructive interference. *if it were destructive interference then this would be odd So, we cancel out pi on both sides and we have the equation 4d / (wavelength) = (even integer) so we solve for wavelength (wavelength) = 4d / (even integer) 4(191nm) / 2 = 382nm ----> not an answer 4(191nm) / 4 = 191nm There are an infinite number of wavelengths that are reflected constructively, that is why you are always given a range in these problems. so, I'll assume the answer is A.... hope this helps, thanks

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