Consider a 400 nm thick film of water (n-1.33) on plastic (-1.9). Visible light is incident. on the film firom air. (25 pts) Sketch this situation and clearly indicate the rays which are interfering with one another. (5 pts) a b. Find three wavelengths that will be reflected brightly from the film. (14 pts) c. Find three wavelengths that will be reflected very dimly, if at all, from the film.

For constructive interference in thin films by reflected light, the condition is

Path difference = 2μd = odd multiple of λ / 2

Where μ is refractive index of water, d is thickness of water medium and λ

is wavelength of light

λ = 4μd or 4μd / 3 or 4μd / 5

= 4 x 1.33 x 400 nm = 2128 nm

or 2128 / 3 = 709.33 nm

or 2128 / 5 = 425.6 nm

For destructive interference (dim reflection)

2μd = multiple of λ = λ or 2λ or 3λ

2 x 1.33 x 400 nm = 1064

or 1064 x 2 = 2128 nm

or 1064 x 3 = 3192 nm.