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What will be the focal length of the eyepiece and the objective lens of a telescope, if the angular magnification of the telescope is given to be 5 for far object. The final image is formed at infinity and the distance between the eyepiece and the objective lens of the telescope is 54 cm. (Focal length of eyepiece = fE; Focal length of objective = fO)
- a)fO = 30 cm, fE = 6 cm
- b)fO = 35 cm, fE = 7 cm
- c)fO = 40 cm, fE = 8 cm
- d)fO = 45 cm, fE = 9 cm
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
What will be the focal length of the eyepiece and the objective lens o...
Given:
Angular magnification, m = 5
Distance between eyepiece and objective lens, d = 54 cm
Final image is formed at infinity
To find:
Focal length of eyepiece, fE and focal length of objective, fO
Formula:
Angular Magnification, m = -fe/fo
Magnifying power of telescope, M = fo/fe
Total Magnification, m' = M x (1 + do/fe)
Where do is the distance between the objective lens and the object.
Calculation:
Let's assume that the distance between the objective lens and the object is very large and can be considered as infinity. Therefore, do ≈ ∞.
Using the formula, m = -fe/fo, we get:
-5 = -fe/fo
fe = fo/5
Using the formula, M = fo/fe, we get:
5 = fo/fe
Substituting the value of fe from the first equation, we get:
5 = fo/(fo/5)
fo = 25 cm
Substituting the value of fo in the first equation, we get:
fe = fo/5
fe = 5 cm
Therefore, the focal length of the eyepiece is 5 cm and the focal length of the objective lens is 25 cm.
Using the formula, m' = M x (1 + do/fe), we get:
m' = 5 x (1 + ∞/5)
m' = 5 x ∞
m' = ∞
Therefore, the total magnification of the telescope is infinite when the final image is formed at infinity.
Hence, the correct answer is option D: fO = 45 cm, fE = 9 cm.
Angular magnification, m = 5
Distance between eyepiece and objective lens, d = 54 cm
Final image is formed at infinity
To find:
Focal length of eyepiece, fE and focal length of objective, fO
Formula:
Angular Magnification, m = -fe/fo
Magnifying power of telescope, M = fo/fe
Total Magnification, m' = M x (1 + do/fe)
Where do is the distance between the objective lens and the object.
Calculation:
Let's assume that the distance between the objective lens and the object is very large and can be considered as infinity. Therefore, do ≈ ∞.
Using the formula, m = -fe/fo, we get:
-5 = -fe/fo
fe = fo/5
Using the formula, M = fo/fe, we get:
5 = fo/fe
Substituting the value of fe from the first equation, we get:
5 = fo/(fo/5)
fo = 25 cm
Substituting the value of fo in the first equation, we get:
fe = fo/5
fe = 5 cm
Therefore, the focal length of the eyepiece is 5 cm and the focal length of the objective lens is 25 cm.
Using the formula, m' = M x (1 + do/fe), we get:
m' = 5 x (1 + ∞/5)
m' = 5 x ∞
m' = ∞
Therefore, the total magnification of the telescope is infinite when the final image is formed at infinity.
Hence, the correct answer is option D: fO = 45 cm, fE = 9 cm.
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Community Answer
What will be the focal length of the eyepiece and the objective lens o...
The image formed by the objective lens will be at the focus of the objective as it is used to focus the far objects.
Let the point of image formation by objective be IO.
Therefore, POIO = fO
Image IO must lie on the first focus of the eyepiece, as the final image is formed at infinity.
Therefore,
PEIO = fE
Therefore, fO + fE = 54 cm
Also, magnification is given to be 5.
Therefore,
Therefore, it is the correct option.
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What will be the focal length of the eyepiece and the objective lens of a telescope, if the angular magnification of the telescope is given to be 5 for far object. The final image is formed at infinity and the distance between the eyepiece and the objective lens of the telescope is 54 cm. (Focal length of eyepiece = fE; Focal length of objective = fO)a)fO = 30 cm, fE = 6 cmb)fO = 35 cm, fE = 7 cmc)fO = 40 cm, fE = 8 cmd)fO = 45 cm, fE = 9 cmCorrect answer is option 'D'. Can you explain this answer?
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What will be the focal length of the eyepiece and the objective lens of a telescope, if the angular magnification of the telescope is given to be 5 for far object. The final image is formed at infinity and the distance between the eyepiece and the objective lens of the telescope is 54 cm. (Focal length of eyepiece = fE; Focal length of objective = fO)a)fO = 30 cm, fE = 6 cmb)fO = 35 cm, fE = 7 cmc)fO = 40 cm, fE = 8 cmd)fO = 45 cm, fE = 9 cmCorrect answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about What will be the focal length of the eyepiece and the objective lens of a telescope, if the angular magnification of the telescope is given to be 5 for far object. The final image is formed at infinity and the distance between the eyepiece and the objective lens of the telescope is 54 cm. (Focal length of eyepiece = fE; Focal length of objective = fO)a)fO = 30 cm, fE = 6 cmb)fO = 35 cm, fE = 7 cmc)fO = 40 cm, fE = 8 cmd)fO = 45 cm, fE = 9 cmCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What will be the focal length of the eyepiece and the objective lens of a telescope, if the angular magnification of the telescope is given to be 5 for far object. The final image is formed at infinity and the distance between the eyepiece and the objective lens of the telescope is 54 cm. (Focal length of eyepiece = fE; Focal length of objective = fO)a)fO = 30 cm, fE = 6 cmb)fO = 35 cm, fE = 7 cmc)fO = 40 cm, fE = 8 cmd)fO = 45 cm, fE = 9 cmCorrect answer is option 'D'. Can you explain this answer?.
What will be the focal length of the eyepiece and the objective lens of a telescope, if the angular magnification of the telescope is given to be 5 for far object. The final image is formed at infinity and the distance between the eyepiece and the objective lens of the telescope is 54 cm. (Focal length of eyepiece = fE; Focal length of objective = fO)a)fO = 30 cm, fE = 6 cmb)fO = 35 cm, fE = 7 cmc)fO = 40 cm, fE = 8 cmd)fO = 45 cm, fE = 9 cmCorrect answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about What will be the focal length of the eyepiece and the objective lens of a telescope, if the angular magnification of the telescope is given to be 5 for far object. The final image is formed at infinity and the distance between the eyepiece and the objective lens of the telescope is 54 cm. (Focal length of eyepiece = fE; Focal length of objective = fO)a)fO = 30 cm, fE = 6 cmb)fO = 35 cm, fE = 7 cmc)fO = 40 cm, fE = 8 cmd)fO = 45 cm, fE = 9 cmCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What will be the focal length of the eyepiece and the objective lens of a telescope, if the angular magnification of the telescope is given to be 5 for far object. The final image is formed at infinity and the distance between the eyepiece and the objective lens of the telescope is 54 cm. (Focal length of eyepiece = fE; Focal length of objective = fO)a)fO = 30 cm, fE = 6 cmb)fO = 35 cm, fE = 7 cmc)fO = 40 cm, fE = 8 cmd)fO = 45 cm, fE = 9 cmCorrect answer is option 'D'. Can you explain this answer?.
Solutions for What will be the focal length of the eyepiece and the objective lens of a telescope, if the angular magnification of the telescope is given to be 5 for far object. The final image is formed at infinity and the distance between the eyepiece and the objective lens of the telescope is 54 cm. (Focal length of eyepiece = fE; Focal length of objective = fO)a)fO = 30 cm, fE = 6 cmb)fO = 35 cm, fE = 7 cmc)fO = 40 cm, fE = 8 cmd)fO = 45 cm, fE = 9 cmCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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ample number of questions to practice What will be the focal length of the eyepiece and the objective lens of a telescope, if the angular magnification of the telescope is given to be 5 for far object. The final image is formed at infinity and the distance between the eyepiece and the objective lens of the telescope is 54 cm. (Focal length of eyepiece = fE; Focal length of objective = fO)a)fO = 30 cm, fE = 6 cmb)fO = 35 cm, fE = 7 cmc)fO = 40 cm, fE = 8 cmd)fO = 45 cm, fE = 9 cmCorrect answer is option 'D'. Can you explain this answer? tests, examples and also practice JEE tests.
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