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