Class 11 > Unit # 13: Physical Optics > Thin Film Interference

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Interference in Thin Films

Video Lecture: Interference in Thin Films

Watch the complete step-by-step video lecture explaining thin-film interference, phase changes upon reflection, and the derivation of interference conditions:

Interference in Thin Films

“Constructive and destructive interference of light waves is the reason why thin films, such as soap bubbles and oil slicks, show vibrant colorful patterns.”

Thin-film interference occurs due to the superposition of light waves reflecting off the top surface of a transparent film with waves reflecting from its bottom surface. To observe clear and vibrant colored patterns, the thickness of the film must be on the order of the wavelength of light.

Reflection and Phase Change Principles

• Reflection from a Denser Medium: When a transverse light wave strikes the boundary of a optically denser medium, the crest returns as a trough and the trough returns as a crest. This introduces a phase change of $\pi$ radians ($180^\circ$) or an equivalent path difference of $\frac{\lambda}{2}$.
• Reflection from a Rarer Medium: When light strikes the boundary of a rarer medium, the crest returns as a crest and the trough returns as a trough, with no change in phase.

The wavelength of light changes when it enters a medium of refractive index $n$. If $\lambda$ is the wavelength of light in air, its wavelength $\lambda_n$ in a medium of refractive index $n$ is given by:

$\lambda_n = \frac{\lambda}{n}$

Path Difference in Normal Incidence

When light falls normally on a transparent film of thickness $t$, a portion of the light is reflected from the upper surface (Ray 1), experiencing a phase change of $180^\circ$ ($\frac{\lambda}{2}$) because it reflects off a denser medium. Another portion is refracted into the film, reflects off the lower surface (Ray 2) against a rarer boundary (no phase change).

For nearly normal incidence, the extra path traveled by Ray 02 inside the film of thickness $t$ is equal to $2t$. Thus, the optical path difference is:

$\text{Path Difference} = 2nt$ (in terms of film wavelength) or $2t$ (geometrical path difference)

Fig: Interference of light rays reflecting from the upper and lower surfaces of a thin film.

Conditions for Interference in Thin Films

Because there is a $180^\circ$ phase change upon reflection at the top surface, the standard conditions for constructive and destructive interference are reversed.

1. For Constructive Interference (Bright Fringes):

Constructive interference occurs when the total path difference satisfies:

$2nt = \left(m + \frac{1}{2}\right)\lambda \quad \text{where } m = 0, 1, 2, 3, \dots$

2. For Destructive Interference (Dark Fringes):

Destructive interference occurs when the total path difference satisfies:

$2nt = m\lambda \quad \text{where } m = 0, 1, 2, 3, \dots$

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