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A telescope has an objective lens of 10 cm diameter and is situated at a distance of one kilometer from two objects. The minimum distance between these two objects, which can be resolved by the telescope, when the mean wavelength of light is 5000 Å, is of the order of
  • a)
    5 cm
  • b)
    0.5 m
  • c)
    5 m
  • d)
    5 mm
Correct answer is option 'D'. Can you explain this answer?
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A telescope has an objective lens of 10 cm diameter and is situated at...

x is of the order of 5 mm.
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A telescope has an objective lens of 10 cm diameter and is situated at...
To determine the minimum distance that can be resolved by the telescope, we can use the formula for the angular resolution:

θ = 1.22 * (λ / D)

Where:
θ is the angular resolution in radians
λ is the wavelength of light in meters
D is the diameter of the objective lens in meters

Given:
D = 10 cm = 0.1 m
λ = 5000 Å = 5000 * 10^-10 m (converted to meters)

Substituting the values into the formula:

θ = 1.22 * (5000 * 10^-10 / 0.1)

θ ≈ 6.1 * 10^-8 radians

To find the minimum distance that can be resolved, we can use the formula:

d = rθ

Where:
d is the minimum distance that can be resolved
r is the distance between the telescope and the objects

Given:
r = 1 km = 1000 m

Substituting the values into the formula:

d = 1000 * 6.1 * 10^-8

d ≈ 6.1 * 10^-5 meters

Therefore, the minimum distance that can be resolved by the telescope is approximately 6.1 * 10^-5 meters.
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A telescope has an objective lens of 10 cm diameter and is situated at a distance of one kilometer from two objects. The minimum distance between these two objects, which can be resolved by the telescope, when the mean wavelength of light is 5000 Å, is of the order ofa)5 cmb)0.5 mc)5 md)5 mmCorrect answer is option 'D'. Can you explain this answer?
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