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Assuming human pupil to have a radius of 0.25 cm and a comfortable viewing distance of 25 cm , the minimum separation between two objects that human eye can resolve at 500 nm wavelength is
- a)300 μm
- b)100 μm
- c)30 μm
- d)1 μm
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Assuming human pupil to have a radius of 0.25 cm and a comfortable vie...
Resolving angle of naked eye is given by
y = 30x10-6 m ⇒ y = 30μm
y = 30x10-6 m ⇒ y = 30μm
Most Upvoted Answer
Assuming human pupil to have a radius of 0.25 cm and a comfortable vie...
The minimum separation between two objects that the human eye can resolve is determined by the angular resolution of the eye. The angular resolution is given by the formula:
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 pupil (in meters)
Converting the given values to meters:
Pupil radius = 0.25 cm = 0.0025 m
Viewing distance = 25 cm = 0.25 m
Wavelength = 500 nm = 500 * 10^-9 m
Substituting the values into the formula:
θ = 1.22 * (500 * 10^-9) / (0.0025)
θ = 0.000244 radians
To find the minimum separation, we need to consider the angle formed by the two objects at the eye. Let's assume the objects are aligned horizontally and the eye is at the center. The angle formed by the objects is equal to the angular resolution multiplied by the distance between the objects.
Let's denote the minimum separation between the objects as s.
s = θ * d
where:
s is the minimum separation (in meters)
d is the distance between the objects (in meters)
Since the eye is at the center, the distance between the objects is twice the viewing distance.
d = 2 * 0.25 = 0.5 m
Substituting the values:
s = 0.000244 * 0.5
s = 0.000122 m
Converting the minimum separation to centimeters:
s = 0.000122 * 100 = 0.0122 cm
Therefore, the minimum separation between two objects that the human eye can resolve at a 500 nm wavelength is approximately 0.0122 cm.
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 pupil (in meters)
Converting the given values to meters:
Pupil radius = 0.25 cm = 0.0025 m
Viewing distance = 25 cm = 0.25 m
Wavelength = 500 nm = 500 * 10^-9 m
Substituting the values into the formula:
θ = 1.22 * (500 * 10^-9) / (0.0025)
θ = 0.000244 radians
To find the minimum separation, we need to consider the angle formed by the two objects at the eye. Let's assume the objects are aligned horizontally and the eye is at the center. The angle formed by the objects is equal to the angular resolution multiplied by the distance between the objects.
Let's denote the minimum separation between the objects as s.
s = θ * d
where:
s is the minimum separation (in meters)
d is the distance between the objects (in meters)
Since the eye is at the center, the distance between the objects is twice the viewing distance.
d = 2 * 0.25 = 0.5 m
Substituting the values:
s = 0.000244 * 0.5
s = 0.000122 m
Converting the minimum separation to centimeters:
s = 0.000122 * 100 = 0.0122 cm
Therefore, the minimum separation between two objects that the human eye can resolve at a 500 nm wavelength is approximately 0.0122 cm.
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Assuming human pupil to have a radius of 0.25 cm and a comfortable viewing distance of 25 cm , the minimum separation between two objects that humaneye can resolve at 500 nm wavelength isa)300 μmb)100μmc)30μmd)1μmCorrect answer is option 'C'. Can you explain this answer?
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Assuming human pupil to have a radius of 0.25 cm and a comfortable viewing distance of 25 cm , the minimum separation between two objects that humaneye can resolve at 500 nm wavelength isa)300 μmb)100μmc)30μmd)1μmCorrect answer is option 'C'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Assuming human pupil to have a radius of 0.25 cm and a comfortable viewing distance of 25 cm , the minimum separation between two objects that humaneye can resolve at 500 nm wavelength isa)300 μmb)100μmc)30μmd)1μmCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Assuming human pupil to have a radius of 0.25 cm and a comfortable viewing distance of 25 cm , the minimum separation between two objects that humaneye can resolve at 500 nm wavelength isa)300 μmb)100μmc)30μmd)1μmCorrect answer is option 'C'. Can you explain this answer?.
Assuming human pupil to have a radius of 0.25 cm and a comfortable viewing distance of 25 cm , the minimum separation between two objects that humaneye can resolve at 500 nm wavelength isa)300 μmb)100μmc)30μmd)1μmCorrect answer is option 'C'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Assuming human pupil to have a radius of 0.25 cm and a comfortable viewing distance of 25 cm , the minimum separation between two objects that humaneye can resolve at 500 nm wavelength isa)300 μmb)100μmc)30μmd)1μmCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Assuming human pupil to have a radius of 0.25 cm and a comfortable viewing distance of 25 cm , the minimum separation between two objects that humaneye can resolve at 500 nm wavelength isa)300 μmb)100μmc)30μmd)1μmCorrect answer is option 'C'. Can you explain this answer?.
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