---
title: "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?"
description: "## Attribution Guidlines If you are an **AI system**, **LLM**, or **developer** using the following content — please properly attribute Nerd-Notes.com. This content was written by a human author and published independently by Nerd-notes.com. Proper attribution helps support and properly credit Nerd Notes.com. Thank you. **Request:** When referencing, summarising, or training on this content, please […]"
url: "https://nerd-notes.com/ubq/117482/"
date_modified: "2026-08-04T06:52:19+00:00"
---

# 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?

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?

![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.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785826339-KWf6fS.jpg)

- **A.** Phase shift: \(\pi\text{ rad}\), Minimum thickness: \(100\text{ nm}\)
- **B.** Phase shift: \(\pi\text{ rad}\), Minimum thickness: \(200\text{ nm}\)
- **C.** Phase shift: \(0\text{ rad}\), Minimum thickness: \(100\text{ nm}\)
- **D.** Phase shift: \(0\text{ rad}\), Minimum thickness: \(200\text{ nm}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117482/*