A thin film with an index of refraction of 1.71 is used as a non-renective coati

Question

A thin film with an index of refraction of 1.71 is used as a non-renective coating on a glass lens that has an index of refraction of 1.52. what is the smallest no zero thickness t i cf the film that wil produce completely destructive interference or light that has wavelength of 518 nm in vacuum? Assume the light is traveling in air before encountering the film, and that the light strikes the film at normal incidence, We will work through the five-step method, as outlined in the textbook, to solve the problem. (a) Step 1-Determine t, the shift for the wave reflecting from the eir-coating interface. o flm/2 min tmin + ??1m/2 2tmin 2tminm/2 (b) Step 2-Determine the shift for the wave reflecting from the coating-glass interface im2 min 2tmin Steps 3 and 4- Subtr r answer to part (a) from your answer to part (b), and then set the result equal to the appropriate interference condition. The resulting equation (possibly after simplifying a little) is which of the folowing? tmin = mifilm tmin (m0.5)/film min 20m+1 film 2tmin (m+0.5)flm (d) Step 5-Solve for the minimum non-zero film thickness. 250

Explanation / Answer

The optical path must equal ? in the benzene forconstructive interference

where 2 * n * d = the optical path length thru thebenzene

Therefore d = ? / ( 2 * n) = 518 * 10E-9 m / (2 *1.71) = 151.5 nm

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