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The time taken by sunlight to reach the bottom of a tank of depth 4.5 m filled completely with water is ________ ns. The refractive index of water is 4/3.

Asked in GUJCET 2014 · Snell's law, slabs and apparent depth

• (1) 2
• (2) 20
• (3) 1.5
• (4) 200

Step-by-step solution

Why the other options are wrong

• (1) 2 is the answer 2×10⁻⁸ s with the prefix mis-read. 1 ns=10⁻⁹ s, so 2×10⁻⁸ s is 20 ns.
• (3) 1.5 uses the vacuum speed, (4.5)/(3×10⁸)=1.5×10⁻⁸ s, and then reads that as 1.5 ns. Light inside water travels at c/n, not at c.
• (4) 200 ns is 2×10⁻⁷ s, ten times too long; it would need water of refractive index 13.3. Sanity check: t=(nd)/c=((4/3)(4.5))/(3×10⁸)=2×10⁻⁸ s.

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