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The objective of a telescope has a focal length of 1.2 m. It is used to view a 10.0 m tall tower 2 km away. What is the height of the image of the tower formed by the objective?
- a)8 mm
- b)2 mm
- c)6 mm
- d)4 mm
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
The objective of a telescope has a focal length of 1.2 m. It is used t...
α (Radian)=10/2000=1/200rad
α=h/F=h/1.2
h= α x 1.2
h=(1/200) x1.2 cm
=6mm
α=h/F=h/1.2
h= α x 1.2
h=(1/200) x1.2 cm
=6mm
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The objective of a telescope has a focal length of 1.2 m. It is used t...
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The objective of a telescope has a focal length of 1.2 m. It is used t...
Given:
- Focal length of the objective lens (f) = 1.2 m
- Height of the tower (h) = 10.0 m
- Distance between the objective and the tower (d) = 2 km = 2000 m
To find:
- Height of the image of the tower formed by the objective lens
Formula:
The magnification (m) of the telescope is given by:
magnification (m) = -f / (f - d)
The height of the image (h') formed by the objective lens is related to the height of the object (h) and the magnification (m) by the formula:
h' = m × h
Calculation:
1. Substituting the given values in the formula, we can calculate the magnification (m):
m = -f / (f - d)
= -1.2 / (1.2 - 2000)
= -1.2 / (-1998.8)
≈ 0.000601
2. Using the magnification (m) and the height of the tower (h), we can calculate the height of the image (h'):
h' = m × h
≈ 0.000601 × 10.0
≈ 0.00601 m
≈ 6 mm
Answer:
The height of the image of the tower formed by the objective lens is approximately 6 mm. Therefore, the correct answer is option (c) 6 mm.
- Focal length of the objective lens (f) = 1.2 m
- Height of the tower (h) = 10.0 m
- Distance between the objective and the tower (d) = 2 km = 2000 m
To find:
- Height of the image of the tower formed by the objective lens
Formula:
The magnification (m) of the telescope is given by:
magnification (m) = -f / (f - d)
The height of the image (h') formed by the objective lens is related to the height of the object (h) and the magnification (m) by the formula:
h' = m × h
Calculation:
1. Substituting the given values in the formula, we can calculate the magnification (m):
m = -f / (f - d)
= -1.2 / (1.2 - 2000)
= -1.2 / (-1998.8)
≈ 0.000601
2. Using the magnification (m) and the height of the tower (h), we can calculate the height of the image (h'):
h' = m × h
≈ 0.000601 × 10.0
≈ 0.00601 m
≈ 6 mm
Answer:
The height of the image of the tower formed by the objective lens is approximately 6 mm. Therefore, the correct answer is option (c) 6 mm.
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The objective of a telescope has a focal length of 1.2 m. It is used to view a 10.0 m tall tower 2 km away. What is the height of the image of the tower formed by the objective?a)8 mmb)2 mmc)6 mmd)4 mmCorrect answer is option 'C'. Can you explain this answer?
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