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A astronomical telescope has objective and eyepiece of focal lengths 40 cm and 4 cm respectively. To
view an object 200 cm away from the objective, the lenses must be separated by a distance :
- a)54 cm
- b)37.3 cm
- c)46 cm
- d)50 cm
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
A astronomical telescope has objective and eyepiece of focal lengths 4...
Given data:
Focal length of objective lens, f1 = 40 cm
Focal length of eyepiece lens, f2 = 4 cm
Distance of object from objective lens, u = 200 cm
Distance between lenses, d = ?
We can use the formula for the magnifying power of a telescope to find the distance between the lenses. The magnifying power, M is given by:
M = - (f1/f2)
For a telescope in normal adjustment, the final image is formed at infinity. Therefore, the distance between lenses is given by:
1/f1 + 1/f2 = 1/d
Substituting the given values, we get:
1/40 + 1/4 = 1/d
Simplifying the equation, we get:
d = 40/3 cm
Therefore, the distance between the lenses when the final image is formed at infinity is 40/3 cm.
Now, to view an object at a distance of 200 cm from the objective lens, the final image should be formed at the least distance of distinct vision, which is 25 cm.
Using the formula for the distance between lenses, we can find the distance they need to be separated by to form the final image at the least distance of distinct vision:
1/f1 + 1/f2 = 1/d'
Substituting the given values, we get:
1/40 + 1/4 = 1/d'
Simplifying the equation, we get:
d' = 40/3 - 25 = 55/3 = 18.33 cm
Therefore, the distance between the lenses when the final image is formed at the least distance of distinct vision is 18.33 cm.
To find the distance by which the lenses need to be separated, we subtract the two distances:
d - d' = 40/3 - 55/3 = -15/3 = -5 cm
However, since the lenses cannot be separated by a negative distance, we take the absolute value of the difference:
|d - d'| = |-5| = 5 cm
Therefore, the lenses need to be separated by 5 cm to view an object 200 cm away from the objective lens.
However, the given options do not match with the answer obtained. Therefore, the correct answer cannot be determined from the given options.
Focal length of objective lens, f1 = 40 cm
Focal length of eyepiece lens, f2 = 4 cm
Distance of object from objective lens, u = 200 cm
Distance between lenses, d = ?
We can use the formula for the magnifying power of a telescope to find the distance between the lenses. The magnifying power, M is given by:
M = - (f1/f2)
For a telescope in normal adjustment, the final image is formed at infinity. Therefore, the distance between lenses is given by:
1/f1 + 1/f2 = 1/d
Substituting the given values, we get:
1/40 + 1/4 = 1/d
Simplifying the equation, we get:
d = 40/3 cm
Therefore, the distance between the lenses when the final image is formed at infinity is 40/3 cm.
Now, to view an object at a distance of 200 cm from the objective lens, the final image should be formed at the least distance of distinct vision, which is 25 cm.
Using the formula for the distance between lenses, we can find the distance they need to be separated by to form the final image at the least distance of distinct vision:
1/f1 + 1/f2 = 1/d'
Substituting the given values, we get:
1/40 + 1/4 = 1/d'
Simplifying the equation, we get:
d' = 40/3 - 25 = 55/3 = 18.33 cm
Therefore, the distance between the lenses when the final image is formed at the least distance of distinct vision is 18.33 cm.
To find the distance by which the lenses need to be separated, we subtract the two distances:
d - d' = 40/3 - 55/3 = -15/3 = -5 cm
However, since the lenses cannot be separated by a negative distance, we take the absolute value of the difference:
|d - d'| = |-5| = 5 cm
Therefore, the lenses need to be separated by 5 cm to view an object 200 cm away from the objective lens.
However, the given options do not match with the answer obtained. Therefore, the correct answer cannot be determined from the given options.
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A astronomical telescope has objective and eyepiece of focal lengths 40 cm and 4 cm respectively. Toview an object 200 cm away from the objective, the lenses must be separated by a distance :a)54 cmb)37.3 cmc)46 cmd)50 cmCorrect answer is option 'A'. Can you explain this answer?
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A astronomical telescope has objective and eyepiece of focal lengths 40 cm and 4 cm respectively. Toview an object 200 cm away from the objective, the lenses must be separated by a distance :a)54 cmb)37.3 cmc)46 cmd)50 cmCorrect answer is option 'A'. 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 astronomical telescope has objective and eyepiece of focal lengths 40 cm and 4 cm respectively. Toview an object 200 cm away from the objective, the lenses must be separated by a distance :a)54 cmb)37.3 cmc)46 cmd)50 cmCorrect answer is option 'A'. 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 astronomical telescope has objective and eyepiece of focal lengths 40 cm and 4 cm respectively. Toview an object 200 cm away from the objective, the lenses must be separated by a distance :a)54 cmb)37.3 cmc)46 cmd)50 cmCorrect answer is option 'A'. Can you explain this answer?.
A astronomical telescope has objective and eyepiece of focal lengths 40 cm and 4 cm respectively. Toview an object 200 cm away from the objective, the lenses must be separated by a distance :a)54 cmb)37.3 cmc)46 cmd)50 cmCorrect answer is option 'A'. 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 astronomical telescope has objective and eyepiece of focal lengths 40 cm and 4 cm respectively. Toview an object 200 cm away from the objective, the lenses must be separated by a distance :a)54 cmb)37.3 cmc)46 cmd)50 cmCorrect answer is option 'A'. 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 astronomical telescope has objective and eyepiece of focal lengths 40 cm and 4 cm respectively. Toview an object 200 cm away from the objective, the lenses must be separated by a distance :a)54 cmb)37.3 cmc)46 cmd)50 cmCorrect answer is option 'A'. Can you explain this answer?.
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