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Light traveling from water to a gemstone strikes the surface at an angle of 80.0º and has an angle of refraction of 15.2º . (a) What is the
Question
Light traveling from water to a gemstone strikes the surface at an angle of 80.0º and has an angle of refraction of 15.2º . (a) What is the speed of light in the gemstone? (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?
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Physics
3 years
2021-08-02T21:20:43+00:00
2021-08-02T21:20:43+00:00 1 Answers
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Answers ( )
Answer:
a
The the speed of light in the gemstone is![Rendered by QuickLaTeX.com v= 0.599*10^8 m/s](https://documen.tv/wp-content/ql-cache/quicklatex.com-ddc3d185a4f1dd36ac20e7b72de9dae1_l3.png)
b
The unreasonable thing about this is that the speed of ligth in the gemstone is too low
the speed is 19% of the speed of light which is very low
c
One main unreasonable or inconsistent factor is that the assumption that the differnce between the angle of incidence and angle of refraction is very large
Explanation:
From the question we are told that
The angle of incidence![Rendered by QuickLaTeX.com i = 80^o](https://documen.tv/wp-content/ql-cache/quicklatex.com-e1ecbae763178ae1046eb5cf378541d5_l3.png)
The angle of refraction![Rendered by QuickLaTeX.com r = 15.2^o](https://documen.tv/wp-content/ql-cache/quicklatex.com-d8bcd9ea3187918c0ba17aee2e197b58_l3.png)
From Snell’s law we have ,
Where
is the refractive index of the first medium (water) with a constant value of ![Rendered by QuickLaTeX.com n_1 = 1..333](https://documen.tv/wp-content/ql-cache/quicklatex.com-2f3eee9492eecd85f14735f7975b4c59_l3.png)
Making the
the subject of the formula
Generally refractive index of a material is mathematically represented
Where c is the speed light
v is the speed of light observed in a medium
Making v the subject
substituting value for gem stone