Calculating the Longest Visible Wavelength for Thin Film Interference

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The discussion focuses on calculating the longest visible wavelength for thin film interference involving an oil film on water. The film's thickness is 360 nm, and the indices of refraction are 1.48 for oil and 1.33 for water. For constructive interference, the longest visible wavelength is calculated using the equation λ=2t/(m + 1/2), yielding approximately 456.24 nm. The second part of the discussion addresses the longest wavelength for strong transmission, suggesting the use of the equation 2tn = m λ. Additionally, the reflectance equation R= ((n2-n1)/(n2+n1))^2 is mentioned in relation to minimum reflectance conditions.
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Homework Statement


An oil film (index of refraction no = 1.48) floating on water (index of refraction nw = 1.33) is illuminated from above by white light at normal incidence. The film is 360.0 nm thick.



What is the longest visible wavelength that will be strongly reflected?

What is the longest visible wavelength that will be strongly transmitted?

Homework Equations



2nt = (m + 1/2)λ--constructive
2tn = m λ, with m = 0,1,2,...

The Attempt at a Solution


since visible range=400 - 700 nanometers
the longest visible wavelength for constructive interference ...should it be λ=2t/(2+1/2)
λ=456.24?
and so for the second question i use the second equation?
 
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Do you know the equation for reflectance? I think if the thickness of the film is 1/4λ then the reflectance is minimum.
 
R= ((n2-n1)/(n2+n1))^2
is it this one?
 

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