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Question
Choose the correct option.
There are different fish, monkeys, and water of the habitable planet of the star Proxima b. A fish swimming underwater feels that there is a monkey at 2.5 m on the top of a tree. The same monkey feels that the fish is 1.6 m below the water surface. Interestingly, height of the tree and the depth at which the fish is swimming are exactly same. Refractive index of that water must be
Options
`6/5`
`5/4`
`4/3`
`7/5`
Solution
`5/4`
Explanation:
As, height of the tree = depth at which fish swimming, Real depth, or height in both conditions is same, (say) x.
∴ For monkey, as apparent depth = 1.6 m,
`"n"_"water"/"n"_"air"="Real depth"/"Apparent depth"="x"/1.6`
For fish, as apparent height = 2.5 m,
`"n"_"air"/"n"_"water"="Real height"/"Apparent height"="x"/2.5`
∴ `"x"/1.6xx"x"/2.5` = 1
∴ x2 = 4 ⇒ x = 2
∴ `"n"_"water"/"n"_"air"="x"/1.6=2/1.6=5/4`
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