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A tank is filled with water to a height of 15.5 cm. The apparent depth of a needle lying at the bottom of the tank is measured by a microscope to be 8.5 cm. If water is replaced by a liquid of refractive index 1.94 upto the same height, by what distance would the microscope have to be moved to focus on the needle again ?
  • a)
    1.00 cm
  • b)
    2.37 cm
  • c)
    0.51 cm
  • d)
    3.93 cm
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
A tank is filled with water to a height of 15.5 cm. The apparent depth...
Actual depth of the needle in water
h1 = 15.5cm
Apparent depth of needle in water h2 = 8.5cm
For another liquid with μ' = 1.94
Apparent depth, H = 15.5/1.94 = 7.99cm
Here, H is less than h2. Thus to focus the needle again, the microscope should be moved up by the distance 8.5 − 7.99 = 0.51cm
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Most Upvoted Answer
A tank is filled with water to a height of 15.5 cm. The apparent depth...
Given:
- Height of water in the tank = 15.5 cm
- Apparent depth of the needle in water = 8.5 cm
- Refractive index of the liquid = 1.94

To find:
The distance by which the microscope has to be moved to focus on the needle again.

Concept:
The apparent depth of an object immersed in a liquid is given by the formula:
Apparent depth = Actual depth / Refractive index of the liquid

Calculation:
1. In the first case, when the tank is filled with water:
- Actual depth of the needle = 15.5 cm
- Apparent depth of the needle = 8.5 cm

2. Using the formula, we can write:
8.5 cm = 15.5 cm / Refractive index of water
Refractive index of water = 15.5 cm / 8.5 cm
Refractive index of water = 1.82

3. In the second case, when the water is replaced by a liquid with refractive index 1.94:
- Actual depth of the needle = 15.5 cm
- Refractive index of the liquid = 1.94

4. Using the formula, we can write:
Apparent depth of the needle = Actual depth of the needle / Refractive index of the liquid
Apparent depth of the needle = 15.5 cm / 1.94
Apparent depth of the needle = 8 cm (approximately)

5. The microscope needs to be moved by the difference in apparent depths in the two cases:
Distance to be moved = Apparent depth in the second case - Apparent depth in the first case
Distance to be moved = 8 cm - 8.5 cm
Distance to be moved = -0.5 cm (approximately)

6. The negative sign indicates that the microscope needs to be moved in the opposite direction. Taking the absolute value, the distance to be moved is 0.5 cm.

Therefore, the microscope needs to be moved by 0.5 cm to focus on the needle again.

Answer:
The correct answer is option (c) 0.51 cm.
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Read the following text and answer the following questions on the basis of the same:Electron Microscope Electron microscopes use electrons to illuminate a sample. In Transmission Electron Microscopy (TEM), electrons pass through the sample and illuminate film or a digital camera.Resolution in microscopy is limited to about half of the wavelength of the illumination source used to image the sample. Using visible light the best resolution that can be achieved by microscopes is about ~200 nm. Louis de Broglie showed that every particle or matter propagates like a wave. The wavelength of propagating electrons at a given accelerating voltage can be determined byThus, the wavelength of electrons is calculated to be 3.88 pm when the microscope is operated at 100 keV, 2. 74 pm at 200 keV and 2.24 pm at 300 keV. However, because the velocities of electrons in an electron microscope reach about 70% the speed of light with an accelerating voltage of 200 keV, there are relativistic effects on these electrons. Due to this effect, the wavelength at 100 keV, 200 keV and 300 keV in electron microscopes is 3.70 pm, 2.51 pm and 1.96 pm, respectively.Anyhow, the wavelength of electrons is much smaller than that of photons (2.5 pm at 200 keV). Thus if electron wave is used to illuminate the sample, the resolution of an electron microscope theoretically becomes unlimited. Practically, the resolution is limited to ~0.1 nm due to the objective lens system in electron microscopes. Thus, electron microscopy can resolve subcellular structures that could not be visualized using standard fluorescence microscopy.Q. Wavelength of electron as wave at accelerating voltage 200 keV is

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A tank is filled with water to a height of 15.5 cm. The apparent depth of a needle lying at the bottom of the tank is measured by a microscope to be 8.5 cm. If water is replaced by a liquid of refractive index 1.94 upto the same height, by what distance would the microscope have to be moved to focus on the needle again ?a)1.00 cmb)2.37 cmc)0.51 cmd)3.93 cmCorrect answer is option 'C'. Can you explain this answer?
Question Description
A tank is filled with water to a height of 15.5 cm. The apparent depth of a needle lying at the bottom of the tank is measured by a microscope to be 8.5 cm. If water is replaced by a liquid of refractive index 1.94 upto the same height, by what distance would the microscope have to be moved to focus on the needle again ?a)1.00 cmb)2.37 cmc)0.51 cmd)3.93 cmCorrect answer is option 'C'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A tank is filled with water to a height of 15.5 cm. The apparent depth of a needle lying at the bottom of the tank is measured by a microscope to be 8.5 cm. If water is replaced by a liquid of refractive index 1.94 upto the same height, by what distance would the microscope have to be moved to focus on the needle again ?a)1.00 cmb)2.37 cmc)0.51 cmd)3.93 cmCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A tank is filled with water to a height of 15.5 cm. The apparent depth of a needle lying at the bottom of the tank is measured by a microscope to be 8.5 cm. If water is replaced by a liquid of refractive index 1.94 upto the same height, by what distance would the microscope have to be moved to focus on the needle again ?a)1.00 cmb)2.37 cmc)0.51 cmd)3.93 cmCorrect answer is option 'C'. Can you explain this answer?.
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