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Question
A swimmer inside water looks up at the sky through the surface of the water. The sky is bright due to daylight. He can see ______.
Options
nothing but darkness.
the entire top surface of water bright.
a small illuminated patch directly above his head, whose angular size depends upon the depth of the swimmer in water.
a small illuminated patch directly above his head, whose angular size is independent of the depth of the swimmer.
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Solution
A swimmer inside water looks up at the sky through the surface of the water. The sky is bright due to daylight. He can see a small illuminated patch directly above his head, whose angular size is independent of the depth of the swimmer.
Explanation:
Due to the phenomenon of refraction and the critical angle at the water-air interface, the swimmer can see light from above only within a certain cone (the “Snell’s window”). This angular size of the bright patch is fixed by the refractive indices and does not depend on the swimmer’s depth in water. Outside this cone, total internal reflection occurs, creating darkness outside the illuminated patch.
