Solve the problem using Snell's Law: $\frac { \sin \theta _ { 1 } } { \sin \theta _ { 2 } } = \frac { v _ { 1 } } { v _ { 2 } }$
-A light beam traveling through air makes an angle of incidence of 39° upon a second medium. The refracted beam makes an angle of refraction of 28°. What is the index of refraction of the material of the second medium?
Give the answer to two decimal places.
A) 0.47
B) 0.75
C) 0.63
D) 1.34

Question

Quizplus · Accepted Answer

The index of refraction, $n$, of a medium is related to the speed of light in that medium, $v$, and the speed of light in vacuum, $c$, by the equation $n = \frac{c}{v}$. Snell's Law relates the indices of refraction of two media and the angles of incidence and refraction between these two media as $n_1 \sin \theta_1 = n_2 \sin \theta_2$, where $n_1$ and $n_2$ are the indices of refraction of the first and second media, respectively, and $\theta_1$ and $\theta_2$ are the angles of incidence and refraction, respectively. Given that the light is traveling from air into another medium, we can assume $n_1 = 1$ for air. Thus, the equation simplifies to $\sin \theta_1 = n_2 \sin \theta_2$. Rearranging for $n_2$, we get $n_2 = \frac{\sin \theta_1}{\sin \theta_2}$. Substituting the given angles, $n_2 = \frac{\sin 39^\circ}{\sin 28^\circ}$. Calculating this gives $n_2 \approx 1.34$, which is the index of refraction of the second medium.

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