## Question 5: Explain the interference effect produced by thin films.

A thin film is a layer of transparent medium, like a soap bubble, and is comparable to the wavelength of light. One can see bands of various colors when light falls on such layers.
These bands are produced due to the partial reflection and transmission at the boundary of two media where the wavelength is divided.

Consider a thin wedge-shaped structure of some reflecting medium. A beam of a monochromatic light of wavelength λ is made incident on its surface where it splits in two parts. A part of the beam, say a, is reflected back and another part goes in with some refraction. A portion of this refracted beam is reflected back from the lower surface of the film. We assume this portion is emerging out of thin film as shown in the figure. As the film is very thin, the separation, or the path difference between the two parts of the same beam is quite small. Moreover, both ‘a’ and ‘b’ are parts of the same beam, so they are phase coherent with one another. Therefore, they will superpose with one another and a pattern of alternate bright and dark fringes will be observed.

Now the path difference between ‘a’ and ‘b’ depends upon;

• thickness and nature of the medium
• angle of incidence of the beam

Again we know that when a beam of light moves in a rare medium and reflected by a dense medium,it undergoes a phase change of 180° = π radians after reflection. Similarly, there is no phase change when moving in a denser medium and is reflected from a rare medium.
Applying these conditions to the present situation, ray ‘a’ will reflect from the film surface with a phase change of π radian. However, part ‘b’ of the wave will undergo no change in phase when reflected from the lower surface of the film. Therefore, the reflected parts ‘a’ and ‘b’ will have a phase difference of π radian.
Since both ‘a’ and ‘b’ are parts of the same beam and the path difference is very small, they will superpose with one another and bright and dark fringes will be observed in the region of the reflected parts of the beam.
However, in case of sun light (not monochromatic) incident on a thin film of irregular thickness, we shall observe interference pattern due to each spectral color separately (light has 7 such colors or wavelengths). The reason is that at a certain part of the thin film, the thickness of the film and angle of incidence will provide the required conditions for destructive interference of a particular wavelength (i-e, color… and remember constructive or destructive interference depends of the wavelength, too). This part of the thin film will show the other remaining wavelengths or colors. This means different colors will reinforce or cancel at different places and a rich colorful distribution is viewed. This is the reason we have a rainbow effect for the soap bubbles and oily surfaces.