Solve the Problem $\theta _ { \mathrm { i } }$

Essay

Solve the problem.
-When light travels from one medium to another-from air to water, for instance-it changes direction. (This is why a pencil, partially submerged in water, looks as though it is bent.) The angle of incidence $\theta _ { \mathrm { i } }$ is the angle in the first medium; the angle of refraction $\theta _ { \mathrm { r } }$ is the second medium. (See illustration.) Each medium has an index of refraction $- n _ { i }$ and $n _ { r }$ , respectively-which can be found in tables. Snell's law relates these quantities in the forr
$$\mathrm { n } _ { \mathrm { i } } \sin \theta _ { \mathrm { i } } = \mathrm { n } _ { \mathrm { r } } \sin \theta _ { \mathrm { r } }$$
Solving for $\theta _ { r }$ , we obtain
$$\theta _ { \mathrm { r } } = \sin ^ { - 1 } \left( \frac { \mathrm { n } _ { \mathrm { i } } } { \mathrm { n } _ { \mathrm { r } } } \sin \theta _ { \mathrm { i } } \right)$$
Find $\theta _ { \mathrm { r } }$ for crown glass $\left( \mathrm { n } _ { \mathrm { i } } = 1.52 \right)$ , water( $\left. \mathrm { n } _ { \mathrm { r } } = 1.33 \right)$ , and $\theta _ { \mathrm { i } } = 38 ^ { \circ }$ .