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The magnifying power of a telescope is 9. When it is adjusted for parallel rays, the distance between the objective and eyepiece is found to be 20 cm. The focal lengths of lenses are:​
  • a)
    5 cm, 5 cm
  • b)
    11 cm, 9 cm
  • c)
    10 cm, 10 cm
  • d)
    18 cm, 2 cm
Correct answer is option 'D'. Can you explain this answer?
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Given:
- Magnifying power of the telescope = 9
- Distance between the objective and eyepiece when adjusted for parallel rays = 20 cm

To find:
- Focal lengths of lenses

Solution:
The magnifying power of a telescope is given by the formula:
Magnifying power (M) = -fe/fo
where fe is the focal length of the eyepiece and fo is the focal length of the objective.

Step 1: Find the magnifying power (M) using the given information
Magnifying power (M) = 9

Step 2: Find the ratio of the focal lengths of the objective and eyepiece
M = -fe/fo
9 = -fe/fo
fe/fo = -1/9

Step 3: Use the ratio of the focal lengths to find the actual values of the focal lengths

Given options:
a) 5 cm, 5 cm
b) 11 cm, 9 cm
c) 10 cm, 10 cm
d) 18 cm, 2 cm

Option D: 18 cm, 2 cm
Using the ratio fe/fo = -1/9, we can check if the given focal lengths satisfy this condition.
fe/fo = -1/9
2/18 = -1/9
1/9 = -1/9

Since the ratio is satisfied, the focal lengths of the lenses in option D satisfy the given magnifying power and distance between the objective and eyepiece.

Hence, the correct answer is option D) 18 cm, 2 cm.
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The magnifying power of a telescope is 9. When it is adjusted for parallel rays, the distance between the objective and eyepiece is found to be 20 cm. The focal lengths of lenses are:​a)5 cm, 5 cmb)11 cm, 9 cmc)10 cm, 10 cmd)18 cm, 2 cmCorrect answer is option 'D'. Can you explain this answer?
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