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Two point white dots are 1 mm apart on a black paper. They are viewed by eye of pupil diameter 3 mm. Approximately, what is the maximum distance at which these dots can be resolved by the eye? [Take wavelength of light = 500 nm]
- a)1 m
- b)5 m
- c)3 m
- d)6 m
Correct answer is option 'B'. Can you explain this answer?
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Two point white dots are 1 mm apart on a black paper. They are viewed ...
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Two point white dots are 1 mm apart on a black paper. They are viewed ...
Given:
- Distance between two white dots on black paper = 1 mm
- Diameter of pupil of the eye = 3 mm
- Wavelength of light = 500 nm
To find:
The maximum distance at which these dots can be resolved by the eye.
Explanation:
The ability of the eye to resolve two closely spaced objects is determined by its angular resolution. The angular resolution is the smallest angular separation that the eye can distinguish between two points.
Formula:
The angular resolution (θ) can be calculated using the formula:
θ = 1.22 * (λ / D)
Where:
θ = Angular resolution
λ = Wavelength of light
D = Diameter of the pupil of the eye
Calculation:
Given:
Distance between two white dots = 1 mm = 0.001 m
Diameter of pupil of the eye = 3 mm = 0.003 m
Wavelength of light = 500 nm = 500 * 10^-9 m
Using the formula for angular resolution, we can calculate the maximum angle at which the eye can resolve the dots.
θ = 1.22 * (λ / D)
θ = 1.22 * (500 * 10^-9 / 0.003)
θ ≈ 2.017 * 10^-4 radians
Now, we can use basic trigonometry to find the maximum distance at which the dots can be resolved.
tan(θ) = (Distance between dots) / (Maximum distance)
Maximum distance = (Distance between dots) / tan(θ)
Maximum distance = 0.001 / tan(2.017 * 10^-4)
Maximum distance ≈ 4.958 m
Therefore, the maximum distance at which these dots can be resolved by the eye is approximately 5 meters. Hence, the correct answer is option B.
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Two point white dots are 1 mm apart on a black paper. They are viewed by eye of pupil diameter 3 mm. Approximately, what is the maximum distance at which these dots can be resolved by the eye? [Take wavelength of light = 500 nm]a)1 mb)5 mc)3 md)6 mCorrect answer is option 'B'. Can you explain this answer?
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Two point white dots are 1 mm apart on a black paper. They are viewed by eye of pupil diameter 3 mm. Approximately, what is the maximum distance at which these dots can be resolved by the eye? [Take wavelength of light = 500 nm]a)1 mb)5 mc)3 md)6 mCorrect 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 point white dots are 1 mm apart on a black paper. They are viewed by eye of pupil diameter 3 mm. Approximately, what is the maximum distance at which these dots can be resolved by the eye? [Take wavelength of light = 500 nm]a)1 mb)5 mc)3 md)6 mCorrect 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 point white dots are 1 mm apart on a black paper. They are viewed by eye of pupil diameter 3 mm. Approximately, what is the maximum distance at which these dots can be resolved by the eye? [Take wavelength of light = 500 nm]a)1 mb)5 mc)3 md)6 mCorrect answer is option 'B'. Can you explain this answer?.
Two point white dots are 1 mm apart on a black paper. They are viewed by eye of pupil diameter 3 mm. Approximately, what is the maximum distance at which these dots can be resolved by the eye? [Take wavelength of light = 500 nm]a)1 mb)5 mc)3 md)6 mCorrect 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 point white dots are 1 mm apart on a black paper. They are viewed by eye of pupil diameter 3 mm. Approximately, what is the maximum distance at which these dots can be resolved by the eye? [Take wavelength of light = 500 nm]a)1 mb)5 mc)3 md)6 mCorrect 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 point white dots are 1 mm apart on a black paper. They are viewed by eye of pupil diameter 3 mm. Approximately, what is the maximum distance at which these dots can be resolved by the eye? [Take wavelength of light = 500 nm]a)1 mb)5 mc)3 md)6 mCorrect answer is option 'B'. Can you explain this answer?.
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