Home › Previous year questions › GATE 2017 EC (EC2) › Question 65GATE 2017 EC (EC2) – Question 65 Electromagnetics · Plane Waves and Properties · 2 marks · Numerical answer
Water has optical-frequency permittivity $1.75\epsilon_0$. An isotropic light source at depth d illuminates a circular area of radius 5 m at the surface, as shown. The critical angle is $\theta_c$. The value of d (in metres) is ________.
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Show answer and explanation Correct answer: 4.2 to 4.4
Explanation For nonmagnetic water, the refractive index is $n=\sqrt{1.75}$. Snell's law at critical incidence gives $\sin\theta_c=1/n$.
The surface-circle geometry gives $\tan\theta_c=5/d$. Since $\tan\theta_c=1/\sqrt{n^2-1}$, the depth is $d=5\sqrt{n^2-1}=5\sqrt{0.75}$.
Thus **d=4.3301 m**, within the official 4.2–4.4 m interval.
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