A thin beam of light enters a thick plastic sheet from air at an angle of 32.0° with the normal and continues in the sheet at an angle of 23.0° with the normal.What is the index of refraction of the plastic?
A)0.74
B)1.11
C)1.28
D)1.36

Question

Quizplus · Accepted Answer

The index of refraction of the plastic can be found using Snell's Law, which is $n_1 \sin(\theta_1) = n_2 \sin(\theta_2)$, where $n_1$ and $n_2$ are the indices of refraction of the first and second medium respectively, and $\theta_1$ and $\theta_2$ are the angles of incidence and refraction respectively. Given that the light enters from air (with $n_1 = 1$) at an angle of $32.0^\circ$ and continues in the plastic at an angle of $23.0^\circ$, we can solve for $n_2$, the index of refraction of the plastic, as follows:$$1 \times \sin(32.0^\circ) = n_2 \times \sin(23.0^\circ)$$Solving for $n_2$ gives an index of refraction of approximately 1.36.

A Thin Beam of Light Enters a Thick Plastic Sheet