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Two stars are 10 light years away from the earth. They are seen through a telescope of objective diameter 30 cm.The wavelength of light is 600 nm. To see the stars just resolved by the telescope, the minimum distance between them should be (1 light year=9.46× 1015m) of the order of :
- a)106 km
- b)108 km
- c)1011 km
- d)1010 km
Correct answer is option 'B'. Can you explain this answer?
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Two stars are 10 light years away from the earth. They are seen throug...
To calculate the minimum distance between the stars that can be resolved by the telescope, we can use the formula for the minimum resolvable angle:
θ = 1.22 * (wavelength / diameter)
where θ is the minimum resolvable angle, wavelength is the wavelength of light, and diameter is the diameter of the telescope objective.
First, let's convert the wavelength of light from nanometers to meters:
wavelength = 600 nm = 600 * 10^(-9) m = 6 * 10^(-7) m
Next, we can substitute the values into the formula:
θ = 1.22 * (6 * 10^(-7) m / 0.3 m)
Simplifying, we get:
θ = 1.22 * 2 * 10^(-6)
θ = 2.44 * 10^(-6) radians
Now, we can calculate the minimum distance between the stars:
minimum distance = θ * distance
where distance is the distance between the stars.
Since the stars are 10 light years away from Earth, the distance between them is:
distance = 10 light years * 9.46 * 10^15 m/year = 9.46 * 10^16 m
Substituting the values into the formula:
minimum distance = 2.44 * 10^(-6) * 9.46 * 10^16 m
Simplifying, we get:
minimum distance ≈ 2.31 * 10^11 m
Therefore, the minimum distance between the stars that can be resolved by the telescope is approximately 2.31 * 10^11 meters.
θ = 1.22 * (wavelength / diameter)
where θ is the minimum resolvable angle, wavelength is the wavelength of light, and diameter is the diameter of the telescope objective.
First, let's convert the wavelength of light from nanometers to meters:
wavelength = 600 nm = 600 * 10^(-9) m = 6 * 10^(-7) m
Next, we can substitute the values into the formula:
θ = 1.22 * (6 * 10^(-7) m / 0.3 m)
Simplifying, we get:
θ = 1.22 * 2 * 10^(-6)
θ = 2.44 * 10^(-6) radians
Now, we can calculate the minimum distance between the stars:
minimum distance = θ * distance
where distance is the distance between the stars.
Since the stars are 10 light years away from Earth, the distance between them is:
distance = 10 light years * 9.46 * 10^15 m/year = 9.46 * 10^16 m
Substituting the values into the formula:
minimum distance = 2.44 * 10^(-6) * 9.46 * 10^16 m
Simplifying, we get:
minimum distance ≈ 2.31 * 10^11 m
Therefore, the minimum distance between the stars that can be resolved by the telescope is approximately 2.31 * 10^11 meters.
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Two stars are 10 light years away from the earth. They are seen through a telescope of objective diameter 30 cm.The wavelength of light is 600 nm. To see the stars just resolved by the telescope, the minimum distance between them should be (1 light year=9.46× 1015m) of the order of :a)106 kmb)108 kmc)1011 kmd)1010 kmCorrect answer is option 'B'. Can you explain this answer?
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Two stars are 10 light years away from the earth. They are seen through a telescope of objective diameter 30 cm.The wavelength of light is 600 nm. To see the stars just resolved by the telescope, the minimum distance between them should be (1 light year=9.46× 1015m) of the order of :a)106 kmb)108 kmc)1011 kmd)1010 kmCorrect answer is option 'B'. 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 Two stars are 10 light years away from the earth. They are seen through a telescope of objective diameter 30 cm.The wavelength of light is 600 nm. To see the stars just resolved by the telescope, the minimum distance between them should be (1 light year=9.46× 1015m) of the order of :a)106 kmb)108 kmc)1011 kmd)1010 kmCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two stars are 10 light years away from the earth. They are seen through a telescope of objective diameter 30 cm.The wavelength of light is 600 nm. To see the stars just resolved by the telescope, the minimum distance between them should be (1 light year=9.46× 1015m) of the order of :a)106 kmb)108 kmc)1011 kmd)1010 kmCorrect answer is option 'B'. Can you explain this answer?.
Two stars are 10 light years away from the earth. They are seen through a telescope of objective diameter 30 cm.The wavelength of light is 600 nm. To see the stars just resolved by the telescope, the minimum distance between them should be (1 light year=9.46× 1015m) of the order of :a)106 kmb)108 kmc)1011 kmd)1010 kmCorrect answer is option 'B'. 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 Two stars are 10 light years away from the earth. They are seen through a telescope of objective diameter 30 cm.The wavelength of light is 600 nm. To see the stars just resolved by the telescope, the minimum distance between them should be (1 light year=9.46× 1015m) of the order of :a)106 kmb)108 kmc)1011 kmd)1010 kmCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two stars are 10 light years away from the earth. They are seen through a telescope of objective diameter 30 cm.The wavelength of light is 600 nm. To see the stars just resolved by the telescope, the minimum distance between them should be (1 light year=9.46× 1015m) of the order of :a)106 kmb)108 kmc)1011 kmd)1010 kmCorrect answer is option 'B'. Can you explain this answer?.
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