Thin-film Interference
Thin-film interference is a phenomenon of two or more light waves superposition which causes their mutual amplification or reduction depending on how the phases of these waves are related to each other. A light beam 1 with a wavelength (λ) falls on the film at an angel (α) and is reflected at the point A. A light beam 2 travels in the film, is reflected from its lower boundary at the point B, is refracted at the point C and returns into the air (fig.1). The path difference appears between two adjacent reflected beams 1 and 2. A light beam 1 passes the distance equal to the interval ABC multiplied by the refractive index (n). But at the point C a part of the light beam is reflected down again, at the point В1 is reflected up, etc. Thus the connection of many waves occurs as a result of consequent reflections of incident light from the lower boundary of the transparent film. This calls multiple beam interference.
If the interval ABC is a whole number of wavelengths, their peaks and troughs will coincide and amplification of all the reflected waves will occur (interference maximum). When the film is illuminated by white light, consisting of waves of different frequency and length, light is refracted at the boundary between the media, and a part of the spectrum is eliminated. The interference maximum occurs for a specific wavelength (red, green or blue) at a certain film thickness and angle. In reflected light the film will have a color corresponding to a certain wavelength. This phenomenon is called “colors in thin films”.
Fig. 1. Multiple beam interference scheme:
λ — wavelength of incident light; α — angle of incidence; β — refraction angle; n — refractive index; h — thickness of the film.Conditions of the interference maximum: coincidence of peaks and troughs (phase) of waves 1, 2, 3
Fig. 2. Colours in thin films.
The interval ABC is equal to the length of a red light — interference maximum is achieved, phases of reflected and refracted waves are equal.The film is coloured red