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A telescope has an objective lens of 10 cm diameter and is situated at a distance of 1 kilometre 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 angstrom is of the order?
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A telescope has an objective lens of 10 cm diameter and is situated at...
The power of resolution of the telescope is given by:Δθ≈1.22 λ2awhere, a = radius of the lensetherefore,Δθ = 1.22 x5000x10−1010x10−2 (since the diameter is give in the question)Δθ = 6.1x10−6 radiansNow,Δθ = arc radius = minimum distance between the two points distance between the telescope and the location of two points 6.1x10−6 = minimum distance between the two points 103minimum distance between the two points = 6.1x10−3 m6.1x10−3 m is the minimum distance that the telescope will be able to resolve at that distance.The power of resolution of the telescope is given by:∆θ≈1.22 λ2awhere, a = radius of the lensetherefore,∆θ = 1.22 x5000x10-1010x10-2 (since the diameter is give in the question)∆θ = 6.1x10-6 radiansNow,∆θ = arc radius = minimum distance between the two points distance between the telescope and the location of two points 6.1x10-6 = minimum distance between the two points 103minimum distance between the two points = 6.1x10-3 m6.1x10-3 m is the minimum distance that the telescope will be able to resolve at that distance.
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A telescope has an objective lens of 10 cm diameter and is situated at...
Objective:
To calculate the minimum distance between two objects that can be resolved by a telescope with a given objective lens diameter and distance from the objects.
Given:
- Objective lens diameter: 10 cm
- Distance from the objects: 1 kilometer
- Mean wavelength of light: 5000 angstroms
Formula:
The minimum resolvable angle (θ) can be calculated using the formula:
θ = 1.22 * (λ / D)
Where:
- θ is the minimum resolvable angle in radians
- λ is the wavelength of light in meters
- D is the diameter of the objective lens in meters
Calculations:
1. Converting the objective lens diameter to meters:
10 cm = 0.1 meters
2. Converting the mean wavelength of light to meters:
5000 angstroms = 5000 * 10^(-10) meters = 5 * 10^(-7) meters
3. Substituting the values into the formula to calculate the minimum resolvable angle:
θ = 1.22 * (5 * 10^(-7) / 0.1)
4. Simplifying the equation:
θ = 1.22 * 5 * 10^(-6)
5. Calculating the minimum resolvable angle:
θ ≈ 6.1 * 10^(-6) radians
6. The minimum distance (Dmin) between two objects that can be resolved by the telescope can be calculated using the formula:
Dmin = R * θ
Where R is the distance from the objects to the telescope.
7. Substituting the values into the formula to calculate the minimum distance:
Dmin = 1000 * 6.1 * 10^(-6)
8. Simplifying the equation:
Dmin ≈ 6.1 meters
Answer:
The minimum distance between the two objects that can be resolved by the telescope is approximately 6.1 meters.
To calculate the minimum distance between two objects that can be resolved by a telescope with a given objective lens diameter and distance from the objects.
Given:
- Objective lens diameter: 10 cm
- Distance from the objects: 1 kilometer
- Mean wavelength of light: 5000 angstroms
Formula:
The minimum resolvable angle (θ) can be calculated using the formula:
θ = 1.22 * (λ / D)
Where:
- θ is the minimum resolvable angle in radians
- λ is the wavelength of light in meters
- D is the diameter of the objective lens in meters
Calculations:
1. Converting the objective lens diameter to meters:
10 cm = 0.1 meters
2. Converting the mean wavelength of light to meters:
5000 angstroms = 5000 * 10^(-10) meters = 5 * 10^(-7) meters
3. Substituting the values into the formula to calculate the minimum resolvable angle:
θ = 1.22 * (5 * 10^(-7) / 0.1)
4. Simplifying the equation:
θ = 1.22 * 5 * 10^(-6)
5. Calculating the minimum resolvable angle:
θ ≈ 6.1 * 10^(-6) radians
6. The minimum distance (Dmin) between two objects that can be resolved by the telescope can be calculated using the formula:
Dmin = R * θ
Where R is the distance from the objects to the telescope.
7. Substituting the values into the formula to calculate the minimum distance:
Dmin = 1000 * 6.1 * 10^(-6)
8. Simplifying the equation:
Dmin ≈ 6.1 meters
Answer:
The minimum distance between the two objects that can be resolved by the telescope is approximately 6.1 meters.
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A telescope has an objective lens of 10 cm diameter and is situated at a distance of 1 kilometre 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 angstrom is of the order?
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A telescope has an objective lens of 10 cm diameter and is situated at a distance of 1 kilometre 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 angstrom is of the order? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A telescope has an objective lens of 10 cm diameter and is situated at a distance of 1 kilometre 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 angstrom is of the order? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A telescope has an objective lens of 10 cm diameter and is situated at a distance of 1 kilometre 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 angstrom is of the order?.
A telescope has an objective lens of 10 cm diameter and is situated at a distance of 1 kilometre 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 angstrom is of the order? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A telescope has an objective lens of 10 cm diameter and is situated at a distance of 1 kilometre 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 angstrom is of the order? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A telescope has an objective lens of 10 cm diameter and is situated at a distance of 1 kilometre 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 angstrom is of the order?.
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