Solve the problem using Snell's Law: $$\frac { \sin \theta _ { 1 } } { \sin \theta _ { 2 } } = \frac { v _ { 1 } } { v _ { 2 } }$$
-The index of refraction of light passing from air into a second medium is $1.67$. If the angle of incidence is $87 ^ { \circ }$, what is the angle of refraction (to two decimal places)?
A) $54.31 ^ { \circ }$
B) $53.27 ^ { \circ }$
C) $36.73 ^ { \circ }$
D) $35.69 ^ { \circ }$

Question

Quizplus · Accepted Answer

The index of refraction, $n$, is related to the velocity of light in the medium by $n = \frac{c}{v}$, where $c$ is the speed of light in a vacuum. Snell's Law can also be written as $n_1 \sin \theta_1 = n_2 \sin \theta_2$. Given $n_1 = 1$ (for air), $n_2 = 1.67$, and $\theta_1 = 87^\circ$, we can solve for $\theta_2$. Rearranging for $\theta_2$, we get $\sin \theta_2 = \frac{n_1}{n_2} \sin \theta_1$. Substituting the given values, $\sin \theta_2 = \frac{1}{1.67} \sin 87^\circ$. Calculating this gives $\sin \theta_2 \approx 0.599$, and taking the arcsin gives $\theta_2 \approx 36.73^\circ$.

Solve the Problem Using Snell's Law sin⁡θ1sin⁡θ2=v1v2\frac { \sin \theta _ { 1 } } { \sin \theta _ { 2 } } = \frac { v _ { 1 } } { v _ { 2 } }sinθ2​sinθ1​​=v2​v1​​

Solve the Problem Using Snell's Law $\frac { \sin \theta _ { 1 } } { \sin \theta _ { 2 } } = \frac { v _ { 1 } } { v _ { 2 } }$