A model of an optical fiber is shown in the figure below. The optical fiber has an index of refraction, n, and is surrounded by free space. What angles of incidence, θ, will result in the light being totally internally reflected at the second surface ?

Engineering

Physics

Curved Surface Refraction

Plane Surface Refraction

Total Internal Reflection

Question

A model of an optical fiber is shown in the figure below. The optical fiber has an index of refraction, n, and is surrounded by free space. What angles of incidence, θ, will result in the light being totally internally reflected at the second surface ?

$θ < \sin^{- 1} (\sqrt{n^{2} + 1})$

$θ < \sin^{- 1} (\sqrt{n^{2} - 1})$

$\sin^{- 1} (\sqrt{n^{2} - 1}) < θ < \sin^{- 1} (\sqrt{n^{2} + 1})$

$θ > \sin^{- 1} (\sqrt{n^{2} - 1})$

LiveFree JEE Main Previous Year Online Papers Live Free JEE Advance Previous Year Online Papers

College PredictorLive

Know your College Admission Chances Based on your Rank/Percentile, Category and Home State.

Get your JEE Main Personalised Report with Top Predicted Colleges in JoSA

φ > φ_c
sin φ > sin φ_c
$\cos α > \frac{1}{n}$ ..... (i)
sin θ = n sin α
$\frac{\sin θ}{n} = \sin α$ ..... (ii)
$\begin{aligned} \sin θ < \sqrt{n^{2} - 1} \\ θ < \sin^{- 1} \sqrt{n^{2} - 1} \end{aligned}$