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A Tank is Filled with Water to a Height of 12.5 Cm What is the Refractive Index of Water? If Water is Replaced by a Liquid of Refractive Index 1.63 up to the Same Height, by What Distance Would the Microscope Have to Be Moved to Focus on the Needle Again - Physics

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

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Actual depth of the needle in water, h1 = 12.5 cm

Apparent depth of the needle in water, h2 = 9.4 cm

Refractive index of water = μ

The value of μcan be obtained as follows:

`mu = h_1/h_2`

`= 12.5/9.4 ~~ 1.33`

Hence, the refractive index of water is about 1.33.

Water is replaced by a liquid of refractive index, `mu^' = 1.63`

The actual depth of the needle remains the same, but its apparent depth changes. Let y be the new apparent depth of the needle. Hence, we can write the relation:

`mu' = h_1/y`

`:. y = h_1/(mu')`

`= 12.5/1.63 = 7.67 cm`

Hence, the new apparent depth of the needle is 7.67 cm. It is less than h2. Therefore, to focus the needle again, the microscope should be moved up.

∴Distance by which the microscope should be moved up = 9.4 − 7.67

= 1.73 cm

Concept: Refraction
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NCERT Class 12 Physics Textbook
Chapter 9 Ray Optics and Optical Instruments
Q 3 | Page 345
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