A solid glass sphere of refractive index n = 3 and radius R contains a spherical air cavity of radius 2 R , as shown in the figure. A very thin glass layer is present at the point O so that the ai

Question

A solid glass sphere of refractive index $n = 3$ and radius $R$ contains a spherical air cavity of radius $\frac{R}{2}$ , as shown in the figure. A very thin glass layer is present at the point O so that the air cavity (refractive index $n = 1$ ) remains inside the glass sphere. An unpolarized, unidirectional and monochromatic light source $S$ emits a light ray from a point inside the glass sphere towards the periphery of the glass sphere. If the light is reflected from the point O and is fully polarized, then the angle of incidence at the inner surface of the glass sphere is $θ$ . The value of $sin θ$ is ______ [given : θ > 30°]
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TestHub · Accepted Answer

We added a condition θ > 30° to make this question clear for students, otherwise 0.5 and 0.75 both are correct answers

$tan α = 3 α = 6 0^{\circ}$ $3 sin β = 1 \times sin α \Rightarrow β = 3 0^{\circ} \frac{R}{2 sin 3 0 ^{\circ}} = \frac{x}{sin 12 0 ^{\circ}} \frac{R}{sin 12 0 ^{\circ}} = \frac{R 3}{2 \times sin θ} \Rightarrow sin θ = \frac{3}{2} \times \frac{3}{2} sin θ = \frac{3}{4}$

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