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nordsb [41]
3 years ago
7

A fiber-optic rod consists of a central strand of material surrounded by an outer coating. the interior portion of the rod has a

n index of refraction of 1.55. if all rays striking the interior walls of the rod with incident angles greater than 59.5° are subject to total internal reflection, what is the index of refraction of the coating?
Physics
1 answer:
algol133 years ago
5 0

Answer:

the index of refraction of the coating is 1.33  

Explanation:

Given the data in the question;

refraction index of  interior portion of the rod η_{interior = 1.55

angle of incidence θ_i = 59.5°

From Snell's law, we know that;

η_{interior × sinθ_i  = η_{coating × sinθ_r

where η_{interior  is the index of refraction of the rod ( material 1 )

θ_i  is the angle of incidence

η_{coating is the index of refraction in outer coating ( material 2 )

θ_r is the angle of refraction

so we substitute our values into the equation;

η_{interior × sinθ_i  = η_{coating × sinθ_r

1.55 × sin( 59.5° )  = η_{coating × sin( 90° )

1.55 × 0.861629  = η_{coating × 1

1.3355 = η_{coating × 1

η_{coating = 1.33   { 2 decimal places }

Therefore, the index of refraction of the coating is 1.33  

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