At a science museum, Marlow looks down into a display case...

At a science museum, Marlow looks down into a display case and sees two pieces of very flat glass lying on top of each other with light and dark regions on the glass. The exhibit states that monochromatic light with a wavelength of $550 \mathrm{~nm}$ is incident on the glass plates and that the plates are sitting in air. The glass has an index of refraction of 1.51. (a) What is the minimum distance between the two glass plates for one of the dark regions? (b) What is the minimum distance between the two glass plates for one of the light regions? (c) What is the next largest distance between the plates for a dark region? [Hint: Do not worry about the thickness of the glass plates; the thin film is the air between the plates.]

At a science museum, Marlow looks down into a display case and sees two pieces of very flat glass lying on top of each other with light and dark regions on the glass. The exhibit states that monochromatic light with a wavelength of $550 \mathrm{~nm}$ is incident on the glass plates and that the plates are sitting in air. The glass has an index of refraction of 1.51. (a) What is the minimum distance between the two glass plates for one of the dark regions?
(b) What is the minimum distance between the two glass plates for one of the light regions? (c) What is the next largest distance between the plates for a dark region? [Hint: Do not worry about the thickness of the glass plates; the thin film is the air between the plates.]

Key Concepts

Thin Film Interference

Thin film interference occurs when light waves reflect off the upper and lower boundaries of a thin layer (such as an air gap between glass plates) and then interfere with each other. The resulting interference pattern, which can show bright (constructive interference) or dark (destructive interference) fringes, depends on the optical path difference between the two reflected rays.

Optical Path Difference

The optical path difference (OPD) is the product of the physical path length the light travels within a medium and the medium's refractive index. In the context of thin films, the OPD is crucial as it determines the phase difference between light waves, which in turn affects whether they interfere constructively or destructively.

Constructive and Destructive Interference

Constructive interference occurs when the phase difference between two light waves results in their amplitudes adding up, creating bright regions. This typically requires the Optical Path Difference to be an integer multiple of the wavelength (or adjusted by any phase shifts). Conversely, destructive interference happens when the waves are out of phase, canceling each other out and producing dark regions. The conditions for these interferences are central to predicting and understanding the interference patterns.

Phase Shift upon Reflection

When light reflects at a boundary between two media of different refractive indices, it can undergo a phase shift. Typically, a phase shift of ? (half a wavelength) occurs when reflecting from a medium with a higher refractive index than the incident medium. This phase shift must be taken into account when determining the overall phase difference between the interfering waves and is a critical aspect of analyzing thin film interference.

Index of Refraction

The index of refraction is a measure of how much light slows down in a given medium compared to its speed in vacuum. It affects the optical path length and the bending of light at material boundaries. In the context of interference in a thin film, the index of refraction of the material on either side of the film determines the phase shifts on reflection and the effective optical distance the light travels within the film.

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