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

question 253

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 $\theta _ { r }$ 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 $\theta _ { \mathbf { r } }$ , 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 fused quartz $\left( \mathrm { n } _ { \mathrm { i } } = 1.46 \right)$ , ethyl alcohol $\left( \mathrm { n } _ { \mathrm { r } } = 1.36 \right)$ , and $\theta _ { \mathrm { i } } = 8.5 ^ { \circ }$ .
$Solve the problem. -When light travels from one medium to another-from air to water, for instance-it changes direction. (This is why a pencil, partially submerged in water, looks as though it is bent.) The angle of incidence \theta _ { \mathrm { i } } is the angle in the first medium; the angle of refraction \theta _ { r } is the second medium. (See illustration.) Each medium has an index of refraction - n _ { i } and n _ { r } , respectively - which can be found in tables. Snell's law relates these quantities in the forr \mathrm { n } _ { \mathrm { i } } \sin \theta _ { \mathrm { i } } = \mathrm { n } _ { \mathrm { r } } \sin \theta _ { \mathrm { r } } Solving for \theta _ { \mathbf { r } } , we obtain \theta _ { \mathrm { r } } = \sin ^ { - 1 } \left( \frac { \mathrm { n } _ { \mathrm { i } } } { \mathrm { n } _ { \mathrm { r } } } \sin \theta _ { \mathrm { i } } \right) Find \theta _ { \mathrm { r } } for fused quartz \left( \mathrm { n } _ { \mathrm { i } } = 1.46 \right) , ethyl alcohol \left( \mathrm { n } _ { \mathrm { r } } = 1.36 \right) , and \theta _ { \mathrm { i } } = 8.5 ^ { \circ } . a$
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Solve the Problem θi\theta _ { \mathrm { i } }θi​

Definitions:

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