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title: "A thin layer of oil with index of refraction \\(n_{\\text{oil}} = 1.45\\) floats on top of water with index of refraction \\(n_{\\text{water}} = 1.33\\). Monochromatic light traveling in air with index of refraction \\(n_{\\text{air}} = 1.00\\) is incident nearly perpendicular to the top surface of the oil layer. A portion of the light reflects at the air-oil interface, while the transmitted portion travels through the oil layer and reflects at the oil-water interface. Which of the following correctly identifies the phase shifts of the electric field for the two reflected waves relative to their incident waves at each boundary, along with the correct justification?"
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url: "https://nerd-notes.com/ubq/117425/"
date_modified: "2026-08-04T06:52:06+00:00"
---

# A thin layer of oil with index of refraction \(n_{\text{oil}} = 1.45\) floats on top of water with index of refraction \(n_{\text{water}} = 1.33\). Monochromatic light traveling in air with index of refraction \(n_{\text{air}} = 1.00\) is incident nearly perpendicular to the top surface of the oil layer. A portion of the light reflects at the air-oil interface, while the transmitted portion travels through the oil layer and reflects at the oil-water interface. Which of the following correctly identifies the phase shifts of the electric field for the two reflected waves relative to their incident waves at each boundary, along with the correct justification?

A thin layer of oil with index of refraction \(n_{\text{oil}} = 1.45\) floats on top of water with index of refraction \(n_{\text{water}} = 1.33\). Monochromatic light traveling in air with index of refraction \(n_{\text{air}} = 1.00\) is incident nearly perpendicular to the top surface of the oil layer. A portion of the light reflects at the air-oil interface, while the transmitted portion travels through the oil layer and reflects at the oil-water interface. Which of the following correctly identifies the phase shifts of the electric field for the two reflected waves relative to their incident waves at each boundary, along with the correct justification?

![A diagram showing three horizontal layers stacked vertically. The top region is labeled air with n_air = 1.00. Below it, separated by a thin horizontal line representing boundary 1, is a middle layer labeled oil with n_oil = 1.45. Below the oil layer, separated by a second thin horizontal line representing boundary 2, is a bottom region labeled water with n_water = 1.33. An incident light ray drawn as a solid downward arrow in air approaches boundary 1 at a slight angle to the vertical. At boundary 1, a reflected ray drawn as a solid upward arrow returns into the air, and a transmitted ray drawn as a solid downward arrow continues through the oil to boundary 2. At boundary 2, a second reflected ray drawn as a solid upward arrow travels back through the oil. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785826326-gll8kP.jpg)

- **A.** Air-oil reflection: \(\pi \text{ rad}\); oil-water reflection: \(0 \text{ rad}\). Justification: Reflection occurs with a \(\pi \text{ rad}\) phase shift when light reflects off a medium with a greater index of refraction, but with no phase shift when reflecting off a medium with a lower index of refraction.
- **B.** Air-oil reflection: \(\pi \text{ rad}\); oil-water reflection: \(\pi \text{ rad}\). Justification: Reflection at any boundary between two transparent media always causes a \(\pi \text{ rad}\) phase shift in the electric field.
- **C.** Air-oil reflection: \(0 \text{ rad}\); oil-water reflection: \(\pi \text{ rad}\). Justification: Reflection occurs with no phase shift when encountering a medium with a greater index of refraction, but undergoes a \(\pi \text{ rad}\) phase shift when encountering a medium with a lower index of refraction.
- **D.** Air-oil reflection: \(0 \text{ rad}\); oil-water reflection: \(0 \text{ rad}\). Justification: Phase shifts only occur for light transmitted across a boundary, whereas reflected waves always maintain the same phase as the incident wave.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117425/*