Solved GATE papers of EC 2017 Electromagnetics

GATE EC 2017 Electromagnetics Solution

The permittivity of water at optical frequencies is 1.75\varepsilon_0. It is found that an isotropic light source at a distance d under water forms an illuminated circular area of radius 5m as shown in the figure. The critical angle is \theta.

GATE EC 2017 Electromagnetics Solution 10 1 - Grad Plus

The value of d(in meter) is______.

Ans:- 4.33m

Explanation

The light is coming from water to air, so medium 1 is water and medium 2 is air. Thus critical angle is given as-

\theta_c=\sin^{-1}\sqrt{\frac{\in_2}{\in_1}} =\sin^{-1}\sqrt{\frac{\in_0}{1.75\in_0}}=49.1^0

Now if light incident at the water surface with angle more than this angle then it would be totally reflected back into the water.

GATE EC 2017 Electromagnetics Solution 10 2 - Grad Plus
\begin{array}{l}\tan49.1=1.547=\frac5d\\\therefore d=\frac5{1.1547}=4.33\;m\end{array}

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