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[tex]_{interior[/tex] = 1.55
angle of incidence θ[tex]_i[/tex] = 59.5°
From Snell's law, we know that;
η[tex]_{interior[/tex] × sinθ[tex]_i[/tex] = η[tex]_{coating[/tex] × sinθ[tex]_r[/tex]
where η[tex]_{interior[/tex] is the index of refraction of the rod ( material 1 )
θ[tex]_i[/tex] is the angle of incidence
η[tex]_{coating[/tex] is the index of refraction in outer coating ( material 2 )
θ[tex]_r[/tex] is the angle of refraction
so we substitute our values into the equation;
η[tex]_{interior[/tex] × sinθ[tex]_i[/tex] = η[tex]_{coating[/tex] × sinθ[tex]_r[/tex]
1.55 × sin( 59.5° ) = η[tex]_{coating[/tex] × sin( 90° )
1.55 × 0.861629 = η[tex]_{coating[/tex] × 1
1.3355 = η[tex]_{coating[/tex] × 1
η[tex]_{coating[/tex] = 1.33 { 2 decimal places }
Therefore, the index of refraction of the coating is 1.33
