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 - Physics

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Numerical

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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Solution

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:

μ = `"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, μ' = 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:

μ' = `"h"_1/"y"`

∴ y = `"h"_1/(μ"'")`

= `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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Chapter 9: Ray Optics and Optical Instruments - Exercise [Page 344]

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NCERT Physics Class 12
Chapter 9 Ray Optics and Optical Instruments
Exercise | Q 9.3 | Page 344
NCERT Physics Class 12
Chapter 9 Ray Optics and Optical Instruments
Exercise | Q 3 | Page 345

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