Light in air is initially traveling parallel to the face AC of an equilateral triangular prism, as shown in the figure. The prism is made of glass with an index of refraction of 1.52. If the light does not strike the face AC, what is the angle between the ray as it leaves the prism at face BC and the normal in air at that face?
A) 83°
B) 19°
C) 59°
D) 27°
E) 55°

Question

Light in air is initially traveling parallel to the face AC of an equilateral triangular prism, as shown in the figure. The prism is made of glass with an index of refraction of 1.52. If the light does not strike the face AC, what is the angle between the ray as it leaves the prism at face BC and the normal in air at that face? 
A) 83° 
B) 19° 
C) 59° 
D) 27° 
E) 55°

Quizplus · Accepted Answer

We can use Snell's Law to solve this problem. Let the angle of incidence be $	heta_i$ and the angle of refraction be $	heta_r$. Then, we have:

$\sin{	heta_i} = n\sin{	heta_r}$

where $n$ is the refractive index of the prism. Since the prism is equilateral, the angle between faces AB and BC is $60^\circ$. Thus, when the light enters the prism, it is refracted towards the normal, which is perpendicular to face AB. This means that the angle of incidence at face BC is $60^\circ - 	heta_r$. Applying Snell's Law again, we get:

$\sin{(	heta_r)} = \frac{\sin{(60^\circ)}}{n}$

$\Rightarrow \sin{(	heta_r)} = \frac{\sqrt{3}}{2n}$

Using the first equation, we can solve for $\sin{(	heta_i)}$, which is equal to $\sin{(	heta_r)}$:

$\sin{(	heta_i)} = \frac{\sqrt{3}}{2}$

Therefore, we have:

$\sin{	heta_r} = \frac{\sqrt{3}}{2n}$ and $\sin{	heta_i} = \frac{\sqrt{3}}{2}$

Substituting these into the formula for $	heta_r$ in terms of $	heta_i$, we get:

$\frac{\sqrt{3}}{2} = n\sin{(	heta_r)} = \frac{\sqrt{3}}{2}$

Solving for $	heta_r$, we find that $	heta_r = 31.6^\circ$. Finally, the angle between the ray and the normal at face BC is $60^\circ - 	heta_r = 60^\circ - 31.6^\circ = 28.4^\circ$, which is closest to choice A.

Light in Air Is Initially Traveling Parallel to the Face