A beam of light, traveling in air, strikes a plate of transparent material at an angle of incidence of $56.0 ^ { \circ }$. It is observed that the reflected and refracted beams form an angle of $90.0 ^ { \circ }$. What is the index of refraction of this material?
A) $1.48$
B) $1.43$
C) $1.44$
D) $1.40$

Question

Quizplus · Accepted Answer

The angle of refraction can be found using the fact that the reflected and refracted beams form a right angle. Given the angle of incidence is $56.0^\circ$, and the reflected and refracted beams form a $90.0^\circ$ angle, the angle of refraction ($\theta_r$) is $34.0^\circ$ because $90.0^\circ - 56.0^\circ = 34.0^\circ$. Using Snell's law, $n_1 \sin(\theta_1) = n_2 \sin(\theta_2)$, where $n_1 = 1$ (for air), $\theta_1 = 56.0^\circ$, and $\theta_2 = 34.0^\circ$, we can solve for $n_2$, the index of refraction of the material. Plugging in the values, we find $n_2 = \frac{\sin(56.0^\circ)}{\sin(34.0^\circ)} \approx 1.48$.

A Beam of Light, Traveling in Air, Strikes a Plate 56.0∘56.0 ^ { \circ }56.0∘

A Beam of Light, Traveling in Air, Strikes a Plate $56.0 ^ { \circ }$