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Question

A light wave enters from I medium into II medium. Its velocity in second medium is double that in I medium. For the phenomenon of total internal reflection to take place the angle of incidence must be greater than a certain value. This value is


A
20o
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B
30o
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C
45o
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D
60o
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Solution

The correct option is B $$30^o$$
Since velocity of light wave is inversely proportional to refractive index of medium. So the refractive index of second medium is half of the medium 1.
$$\eta_1=2\eta_2$$  
For total internal reflection the incident rays from denser medium should be
greater than critical angle,
$$\eta_1 sin\theta_c=\eta_2=\dfrac{\eta_1}{2}$$ 
So $$sin \theta_c = 0.5$$
So $$\theta_c=30^o$$

Physics

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