A tank is filled with water to a height of 12.5cm. The apparent depth of a needle lying at the bottom of the tank is measured by a microscope to be 9.4cm. 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?
A tank is filled with water to a height of 12.5cm. The apparent depth of a needle lying at the bottom of the tank is measured by a microscope to be 9.4cm. 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?
Solution and Explanation
Actual depth of the needle in water,h1=12.5cm
The apparent depth of the needle in water,h2=9.4cm
The refractive index of water = \(\mu\)
The value of μ can be obtained as follows:
\(\mu=\frac{h_1}{h_2}=\frac{12.5}{9.4}\approx1.33\)
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 relationship \(\frac{h_1}{y}\)
∴y=\(\frac{h_1}{\mu'}\)=\(\frac{12.5}{1.63}\)=7.67cm
Hence, the new apparent depth of the needle is 7.67cm.It is less than h2. Therefore,to focus the needle again, the microscope should be moved on.
Distance by which the microscope should be moved up=9.4-7.67=1.73cm.
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Concepts Used:
Ray Optics and Optical Instruments
Optics, deals with the determination of behaviour and the properties of light, along with its interactions with the matter and also with the instruments that are used to detect it.
Ray optics is also known as the geometrical optics and it is a branch of science which describes light propagation.
Reflection is the change in direction of light at an interface in-between two different media so that the wave-front returns into a medium from which it was originated.
Speed of light is the rate at which the light travels in free space.
A phenomenal change in image formed when the light is passed from one medium to another which is called Refraction.
Total Internal Reflection is the reflection of light when the light ray enters into a rarer medium from a denser medium and the angle of incidence is higher than the critical angle of incidence then that light ray will be reflected back to the denser medium.
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