---
title: "An underwater observer looks upward toward the flat surface of a calm body of water with index of refraction \\(n > 1\\). The observer notices a bright circular field of view overhead spanning a cone of half-angle \\(\\theta_c = \\arcsin(1/n)\\) (Snell’s window) containing the entire above-water hemisphere, while the surface outside this cone reflects the underwater surroundings. Which of the following correctly analyzes the origin and behavior of the light reaching the observer’s eye from viewing angles inside (\\(\\theta  \\theta_c\\)) this cone relative to the surface normal?"
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url: "https://nerd-notes.com/ubq/123211/"
date_modified: "2026-09-28T11:57:56+00:00"
---

# An underwater observer looks upward toward the flat surface of a calm body of water with index of refraction \(n > 1\). The observer notices a bright circular field of view overhead spanning a cone of half-angle \(\theta_c = \arcsin(1/n)\) (Snell’s window) containing the entire above-water hemisphere, while the surface outside this cone reflects the underwater surroundings. Which of the following correctly analyzes the origin and behavior of the light reaching the observer’s eye from viewing angles inside (\(\theta  \theta_c\)) this cone relative to the surface normal?

An underwater observer looks upward toward the flat surface of a calm body of water with index of refraction \(n > 1\). The observer notices a bright circular field of view overhead spanning a cone of half-angle \(\theta_c = \arcsin(1/n)\) (Snell's window) containing the entire above-water hemisphere, while the surface outside this cone reflects the underwater surroundings. Which of the following correctly analyzes the origin and behavior of the light reaching the observer's eye from viewing angles inside (\(\theta < \theta_c\)) versus outside (\(\theta > \theta_c\)) this cone relative to the surface normal?

![A 2D cross-sectional diagram showing a horizontal solid line representing a flat water-air interface with air above (n = 1.0) and water below (n > 1). A point labeled 'Observer' is located at a depth below the surface. Two dashed lines extend upward from the Observer to the surface at symmetrical angles \theta_c to a central vertical dashed normal line, defining a cone labeled 'Snell\'s window'. Two light rays in the air approach the surface from opposite horizons nearly parallel to the surface and refract downward along the dashed cone boundaries toward the Observer. A light ray starts underwater from the lower left, travels upward-right toward the surface at an angle greater than \theta_c to the surface normal, and reflects downward toward the Observer. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790596676-J22HS3.jpg)

- **A.** Inside the cone (\(\theta < \theta_c\)), the light originated underwater and underwent total internal reflection; outside the cone (\(\theta > \theta_c\)), the light originated in the air at angles \(\theta_{\text{air}} > \theta_c\) and refracted toward the observer.
- **B.** Inside the cone (\(\theta < \theta_c\)), the light originated in the air across the full \(180^\circ\) above-water hemisphere and refracted into the water; outside the cone (\(\theta > \theta_c\)), the light originated underwater and underwent total internal reflection at the water-air interface.
- **C.** Inside the cone (\(\theta < \theta_c\)), the light originated in the air and underwent total internal reflection at the surface; outside the cone (\(\theta > \theta_c\)), the light originated underwater and refracted along the interface at a \(90^\circ\) angle.
- **D.** Inside the cone (\(\theta < \theta_c\)), the light originated in the air with angles of refraction \(\theta > \theta_c\); outside the cone (\(\theta > \theta_c\)), the light originated underwater and was partially reflected with the majority refracting into the air.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/123211/*