---
title: "A beam of white light containing visible wavelengths from \\(400 \\text{ nm}\\) to \\(700 \\text{ nm}\\) travels inside a transparent glass block toward a boundary with air (index of refraction \\(n_{\\text{air}} = 1.00\\)). The graph shows the critical angle \\(\\theta_c\\) for total internal reflection at the glass-air boundary as a function of wavelength \\(\\lambda\\). The beam strikes the boundary at an angle of incidence of \\(36.9^\\circ\\).  What is the index of refraction of the glass for the longest wavelength of light in the beam that undergoes total internal reflection?  (Note: \\(\\sin 30.0^\\circ = 0.50\\), \\(\\sin 36.9^\\circ = 0.60\\), \\(\\sin 41.8^\\circ = 0.67\\), \\(\\sin 53.1^\\circ = 0.80\\))"
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url: "https://nerd-notes.com/ubq/117466/"
date_modified: "2026-08-04T06:52:14+00:00"
---

# A beam of white light containing visible wavelengths from \(400 \text{ nm}\) to \(700 \text{ nm}\) travels inside a transparent glass block toward a boundary with air (index of refraction \(n_{\text{air}} = 1.00\)). The graph shows the critical angle \(\theta_c\) for total internal reflection at the glass-air boundary as a function of wavelength \(\lambda\). The beam strikes the boundary at an angle of incidence of \(36.9^\circ\).

What is the index of refraction of the glass for the longest wavelength of light in the beam that undergoes total internal reflection?

(Note: \(\sin 30.0^\circ = 0.50\), \(\sin 36.9^\circ = 0.60\), \(\sin 41.8^\circ = 0.67\), \(\sin 53.1^\circ = 0.80\))

A beam of white light containing visible wavelengths from \(400 \text{ nm}\) to \(700 \text{ nm}\) travels inside a transparent glass block toward a boundary with air (index of refraction \(n_{\text{air}} = 1.00\)). The graph shows the critical angle \(\theta_c\) for total internal reflection at the glass-air boundary as a function of wavelength \(\lambda\). The beam strikes the boundary at an angle of incidence of \(36.9^\circ\).

What is the index of refraction of the glass for the longest wavelength of light in the beam that undergoes total internal reflection?

(Note: \(\sin 30.0^\circ = 0.50\), \(\sin 36.9^\circ = 0.60\), \(\sin 41.8^\circ = 0.67\), \(\sin 53.1^\circ = 0.80\))

![A 2D line graph plotting Critical Angle \(\theta_c\) in degrees on the vertical axis versus Wavelength \(\lambda\) in nanometers on the horizontal axis. The vertical axis ranges from 20 to 60 with labeled tick marks at 30.0, 36.9, 41.8, and 53.1. The horizontal axis ranges from 400 to 700 with labeled tick marks at 400, 500, 600, and 700. A smooth, solid curve rises from left to right, passing through four key points: (400, 30.0), (500, 36.9), (600, 41.8), and (700, 53.1). Horizontal and vertical dashed line segments connect each key point to its respective axes. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/fig-critical-angle-vs-wavelength-1785826334-MDmpdL.jpg)

- **A.** \(1.25\)
- **B.** \(1.50\)
- **C.** \(1.67\)
- **D.** \(2.00\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117466/*