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°, what is the angle of refraction (to two decimal places)?
A) 54.31°
B) 53.27°
C) 36.73°
D) 35.69°

Question

Quizplus · Accepted Answer

The index of refraction $n$ is related to the velocity of light in the medium ($v$) and the angle of incidence ($\theta_1$) and refraction ($\theta_2$) by Snell's Law: $n_1 \sin \theta_1 = n_2 \sin \theta_2$. Given $n_1 = 1$ (for air), $n_2 = 1.67$, and $\theta_1 = 87^\circ$, we solve for $\theta_2$. Rearranging Snell's Law gives $\sin \theta_2 = \frac{n_1}{n_2} \sin \theta_1$. Substituting the given values, $\sin \theta_2 = \frac{1}{1.67} \sin 87^\circ$, and solving for $\theta_2$ yields approximately $36.73^\circ$.

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 $\frac { \sin \theta _ { 1 } } { \sin \theta _ { 2 } } = \frac { v _ { 1 } } { v _ { 2 } }$