Questions: A ray in glass (n=1.51) reaches a boundary with air at 49.2 deg. Does it reflect internally or refract into the air? Enter 0 for reflect, and 1 for refract. (Water n=1.33, Air n=1.00)

Solution Steps

We are given:

• The refractive index of glass, \( n_{\text{glass}} = 1.51 \)
• The refractive index of air, \( n_{\text{air}} = 1.00 \)
• The angle of incidence in glass, \( \theta_{\text{glass}} = 49.2^\circ \)

The critical angle \( \theta_c \) is the angle of incidence in the denser medium (glass) for which the angle of refraction in the less dense medium (air) is \( 90^\circ \). It can be calculated using Snell's Law:

\[ n_{\text{glass}} \sin \theta_c = n_{\text{air}} \sin 90^\circ \]

Since \( \sin 90^\circ = 1 \), we have:

\[ \sin \theta_c = \frac{n_{\text{air}}}{n_{\text{glass}}} = \frac{1.00}{1.51} \]

\[ \sin \theta_c = 0.6623 \]

\[ \theta_c = \sin^{-1}(0.6623) \approx 41.1^\circ \]

The angle of incidence \( \theta_{\text{glass}} = 49.2^\circ \) is greater than the critical angle \( \theta_c = 41.1^\circ \).

Since the angle of incidence is greater than the critical angle, total internal reflection occurs, and the ray will reflect internally.

Final Answer