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

question 248

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 $\theta _ { \mathrm { r } }$ 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 $- \mathrm { n } _ { \mathrm { i } }$ and $\mathrm { n } _ { \mathrm { r } }$ , 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 $\theta _ { \mathbf { r } }$ , 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 air $\left( \mathrm { n } _ { \mathrm { i } } = 1.0003 \right)$ , methylene iodide $\left( \mathrm { n } _ { \mathrm { r } } = 1.74 \right)$ , and $\theta _ { \mathrm { i } } = 14.7 ^ { \circ }$ .

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