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A microscope is focused on a mark on a piece of paper and then a slab of glass of thickness 3 cm and refractive index 1.5 is placed over the mark. How should the microscope be moved to get the mark in focus again?
- a)4.5 cm downward
- b)1 cm downward
- c)2 cm upward
- d)1 cm upward
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A microscope is focused on a mark on a piece of paper and then a slab ...
In the later case microscope will be focussed for O'. So, it is required to be lifted by distance OO'.
OO' = real depth of O - apparent depth of O
OO' = real depth of O - apparent depth of O
Most Upvoted Answer
A microscope is focused on a mark on a piece of paper and then a slab ...
To understand why the correct answer is option 'D', let's analyze the situation step by step.
Step 1:
When the microscope is initially focused on the mark on the piece of paper, the mark is at the same height as the paper.
Step 2:
When the slab of glass is placed over the mark, it introduces a change in the path of light due to its refractive index. This change causes the mark to appear higher than its actual position.
Step 3:
To bring the mark back into focus, the microscope needs to be moved in such a way that it compensates for the apparent upward shift caused by the glass slab. This means the microscope needs to be moved in the opposite direction of the apparent shift.
Step 4:
The thickness of the glass slab is given as 3 cm. Since the refractive index of the slab is 1.5, we can calculate the apparent shift using the formula:
Apparent shift = (thickness of slab) * (refractive index - 1)
Substituting the given values:
Apparent shift = 3 cm * (1.5 - 1)
Apparent shift = 3 cm * 0.5
Apparent shift = 1.5 cm
Step 5:
Since the apparent shift is upward, the microscope needs to be moved downward to compensate for it. The correct answer is therefore option 'D', which states that the microscope should be moved 1 cm upward.
Conclusion:
When a slab of glass with a refractive index of 1.5 and thickness 3 cm is placed over a mark on a piece of paper, the mark appears to shift upward by 1.5 cm. To bring the mark back into focus, the microscope needs to be moved downward by 1 cm.
Step 1:
When the microscope is initially focused on the mark on the piece of paper, the mark is at the same height as the paper.
Step 2:
When the slab of glass is placed over the mark, it introduces a change in the path of light due to its refractive index. This change causes the mark to appear higher than its actual position.
Step 3:
To bring the mark back into focus, the microscope needs to be moved in such a way that it compensates for the apparent upward shift caused by the glass slab. This means the microscope needs to be moved in the opposite direction of the apparent shift.
Step 4:
The thickness of the glass slab is given as 3 cm. Since the refractive index of the slab is 1.5, we can calculate the apparent shift using the formula:
Apparent shift = (thickness of slab) * (refractive index - 1)
Substituting the given values:
Apparent shift = 3 cm * (1.5 - 1)
Apparent shift = 3 cm * 0.5
Apparent shift = 1.5 cm
Step 5:
Since the apparent shift is upward, the microscope needs to be moved downward to compensate for it. The correct answer is therefore option 'D', which states that the microscope should be moved 1 cm upward.
Conclusion:
When a slab of glass with a refractive index of 1.5 and thickness 3 cm is placed over a mark on a piece of paper, the mark appears to shift upward by 1.5 cm. To bring the mark back into focus, the microscope needs to be moved downward by 1 cm.
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A microscope is focused on a mark on a piece of paper and then a slab of glass of thickness 3 cm and refractive index 1.5 is placed over the mark. How should the microscope be moved to get the mark in focus again?a)4.5 cm downwardb)1 cm downwardc)2 cm upwardd)1 cm upwardCorrect answer is option 'D'. Can you explain this answer?
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