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AP Physics 2
14.9 Thin-Film Interference
IntermediateMCQMathematicalConceptual22k
A schematic diagram showing a horizontal three-layer medium. The top layer is labeled air with index \(n_{\text{air}} = 1.00\). The middle layer of thickness \(t\) is labeled oil film with index \(n_{\text{oil}} = 1.50\). The bottom layer is labeled water with index \(n_{\text{water}} = 1.33\). A single downward incident light ray in air approaches the top horizontal interface at a slight angle to the normal. At the top interface, Ray 1 reflects upward and to the right into the air. A refracted ray continues downward into the oil layer to the bottom interface, where Ray 2 reflects upward and to the right, exiting back into the air parallel to Ray 1. A vertical double-headed arrow spanning the middle layer is labeled \(t\). No other labels, lines, text, or axes appear.
Reflection of light from a thin oil film floating on water.
A thin layer of oil (\(n_{\text{oil}} = 1.50\)) floats on top of water (\(n_{\text{water}} = 1.33\)). Light with wavelength \(\lambda = 600\text{ nm}\) in air (\(n_{\text{air}} = 1.00\)) is incident nearly perpendicular to the oil film. Ray 1 reflects from the top surface of the oil film, while Ray 2 reflects from the bottom surface at the oil-water boundary, as shown in the diagram. What is the phase shift of Ray 2 upon reflection at the oil-water boundary, and what is the minimum non-zero film thickness \(t\) required for Ray 1 and Ray 2 to interfere constructively?

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