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The focal length of the lenses of an astronomical telescope are 50 cm and 5 cm. The length of the telescope when the image is formed at the least distance of distinct vision is
- a)45 cm
- b)55 cm
- c)275/6 cm
- d)325/6 cm
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
The focal length of the lenses of an astronomical telescope are 50 cm ...
Here, f0 = 50 cm, fe = 5cm, D = 25cm
The length of the telescope when the image is formed at the least distance of distinct vision is
= 325/6 cm
The length of the telescope when the image is formed at the least distance of distinct vision is
= 325/6 cm
Most Upvoted Answer
The focal length of the lenses of an astronomical telescope are 50 cm ...
The focal length of the lenses in an astronomical telescope is given as 50 cm and 5 cm. We need to find the length of the telescope when the image is formed at the least distance of distinct vision.
To solve this problem, we can use the formula for the magnification of a telescope:
Magnification (m) = -f₀/f₁
where f₀ is the focal length of the objective lens and f₁ is the focal length of the eyepiece.
Let's calculate the magnification using the given values:
m = -f₀/f₁ = -50 cm/5 cm = -10
The negative sign indicates that the image formed by the telescope is inverted.
The formula for the total length of a telescope is given by:
Length of telescope = f₀ + f₁
Substituting the given values:
Length of telescope = 50 cm + 5 cm = 55 cm
However, this is not the correct answer because the image formed by the telescope needs to be at the least distance of distinct vision (25 cm for a normal eye).
To find the correct length of the telescope, we can use the formula:
Length of telescope = (m + 1) x least distance of distinct vision
Substituting the values:
Length of telescope = (10 + 1) x 25 cm = 11 x 25 cm = 275 cm
To convert the length to centimeters, we can simplify the fraction:
Length of telescope = 275/1 cm
Simplifying further, we get:
Length of telescope = 275/6 cm
Therefore, the correct answer is option (d) 325/6 cm.
To solve this problem, we can use the formula for the magnification of a telescope:
Magnification (m) = -f₀/f₁
where f₀ is the focal length of the objective lens and f₁ is the focal length of the eyepiece.
Let's calculate the magnification using the given values:
m = -f₀/f₁ = -50 cm/5 cm = -10
The negative sign indicates that the image formed by the telescope is inverted.
The formula for the total length of a telescope is given by:
Length of telescope = f₀ + f₁
Substituting the given values:
Length of telescope = 50 cm + 5 cm = 55 cm
However, this is not the correct answer because the image formed by the telescope needs to be at the least distance of distinct vision (25 cm for a normal eye).
To find the correct length of the telescope, we can use the formula:
Length of telescope = (m + 1) x least distance of distinct vision
Substituting the values:
Length of telescope = (10 + 1) x 25 cm = 11 x 25 cm = 275 cm
To convert the length to centimeters, we can simplify the fraction:
Length of telescope = 275/1 cm
Simplifying further, we get:
Length of telescope = 275/6 cm
Therefore, the correct answer is option (d) 325/6 cm.
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The focal length of the lenses of an astronomical telescope are 50 cm and 5 cm. The length of the telescope when the image is formed at the least distance of distinct vision isa)45 cmb)55 cmc)275/6 cmd)325/6 cmCorrect answer is option 'D'. Can you explain this answer?
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