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The apparent depth of a needle laying a...

The apparent depth of a needle laying at the bottom of the tank, which is filled with water of refractive index `1.33` to a height of `12.5` cm is measured by a microscope to be `9.4 cm`. If water is replaced by a liquid of refractive index `1.63` up to the same height. What distance would the microscope have to be moved to focus on the needle again ?

A

`1.73 cm`

B

`2.13 cm`

C

`1.5 cm`

D

`2.9 cm`

Text Solution

Verified by Experts

The correct Answer is:
A
Apparent depth `= ("Real depth")/(.^(@)mu_(l))`
Here, Real depth `= 12.5 cm` and `.^(a)mu_(l) = 1.63`
`:.` Apparent depth `= (12.5)/(1.63) = 7.67 cm`
Now the microsphere will have to shift from its initial position to focus `9.4 cm` depth object to focus `7.67 cm` depth object.
Shift distance `= 9.4 - 7.67 = 1.73 cm`
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