A) \[\sin \,\theta \ge \frac{13}{11}\]
B) \[\sin \,\theta \ge \frac{11}{13}\]
C) \[\sin \,\theta \ge \frac{\sqrt{3}}{2}\]
D) \[\sin \,\theta \ge \frac{1}{\sqrt{2}}\]
Correct Answer: B
Solution :
Key Idea: Angle of refraction is \[{{90}^{\circ }}\]. From Snell?s law, we have \[_{1}{{\mu }_{2}}=\frac{\sin \,i}{\sin \,r}\] Where \[_{1}{{\mu }_{2}}\] is refractive index of second medium w.r.t. first, \[i\] is angle of incidence and \[r\] is angle of refraction. Given, \[i=\theta ,\,\,r={{90}^{\circ }}\] \[\frac{1.32}{1.56}=\frac{\sin \,\,\theta }{\sin \,\,{{90}^{\circ }}}\] \[\Rightarrow \] \[\sin \,\theta \ge \frac{11}{13}\](for total internal reflection)
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