Question

A 269 nm thin film with index of refraction 1.71 floats on water (with index of refraction 1.333). What is the largest wavelength of reflected light for which constructive interference occur? Answer in units of m (for this part I got 1.84 x 10 ^-6 m)

I need help with the second part of the question: What is the 2nd largest wavelength that interferes constructively? Answer in units of m.

Answer 1

The film thickness for constructive interference has to be 1/4 or 3/4 or 5/4 of the wavelength of the light in the film.

this means for first wavelength

t = 1/4 * _film

t = 1/4 * / n

where n = 1.71

so,

= 4nt

= 4 * 1.71 * 269

= 1.84e-6 m

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for second  largest wavelength that interferes constructively, we take 3/4

so,

t = 3/4 * _film

t = 3/4 * / n

so,

= 4nt / 3

= 4 * 1.71 * 269e-9 / 3

= 6.133 10^-7 m

= 6.133e-7 m ( scientific format)

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