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A paper, with two marks having separation d, isheld normal to the line of sight of an observer ata distance of 50m. The diameter of the eye-lensof the observer is 2 mm. Which of the followingis the least value of d, so that the marks can beseen as separate ? The mean wavelength ofvisible light may be taken as 5000 Å. [2002]
- a)1.25 m
- b)13.6 cm
- c)12.5 cm
- d)2.5 mm
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A paper, with two marks having separation d, isheld normal to the line...
Angular limit of resolution of eye, 
where, d is diameter of eye lens.
Also, if y is the minimum separation between two objects at distance D from eye then
Also, if y is the minimum separation between two objects at distance D from eye then
θ = y/D
Here, wavelength λ = 5000Å = 5x10-7m
D = 50 m
Diameter of eye lens = 2 mm = 2x10-3 m
From eq. (1), minimum separation is
D = 50 m
Diameter of eye lens = 2 mm = 2x10-3 m
From eq. (1), minimum separation is
y = 5 * 10-7 * 50 / 2 * 10-3
y = 0.0125 m
y = 1.25 cm
Most Upvoted Answer
A paper, with two marks having separation d, isheld normal to the line...
We can use the Rayleigh criterion to find the minimum separation between the two marks that can be resolved by the observer:
θ = 1.22 λ/D
where θ is the angular resolution, λ is the wavelength of light, and D is the diameter of the eye's lens. We can rearrange this equation to solve for D:
D = 1.22 λ/θ
We can then use trigonometry to relate the angular resolution to the separation between the marks:
tan(θ) = d/50
where d is the separation between the marks. Rearranging this equation gives:
θ = arctan(d/50)
Substituting this into the equation for D, we get:
D = 1.22 λ/arctan(d/50)
Plugging in the given values, we get:
D = 1.22 * 5000 / arctan(d/50)
Taking the derivative of D with respect to d and setting it equal to zero, we can find the minimum value of d:
d_min = 50 * tan(1.22/(2*sqrt(3)))
d_min ≈ 0.98 mm
Therefore, the least value of d that allows the marks to be seen as separate is approximately 0.98 mm.
θ = 1.22 λ/D
where θ is the angular resolution, λ is the wavelength of light, and D is the diameter of the eye's lens. We can rearrange this equation to solve for D:
D = 1.22 λ/θ
We can then use trigonometry to relate the angular resolution to the separation between the marks:
tan(θ) = d/50
where d is the separation between the marks. Rearranging this equation gives:
θ = arctan(d/50)
Substituting this into the equation for D, we get:
D = 1.22 λ/arctan(d/50)
Plugging in the given values, we get:
D = 1.22 * 5000 / arctan(d/50)
Taking the derivative of D with respect to d and setting it equal to zero, we can find the minimum value of d:
d_min = 50 * tan(1.22/(2*sqrt(3)))
d_min ≈ 0.98 mm
Therefore, the least value of d that allows the marks to be seen as separate is approximately 0.98 mm.
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A paper, with two marks having separation d, isheld normal to the line of sight of an observer ata distance of 50m. The diameter of the eye-lensof the observer is 2 mm. Which of the followingis the least value of d, so that the marks can beseen as separate ? The mean wavelength ofvisible light may be taken as 5000 Å. [2002]a)1.25 mb)13.6 cmc)12.5 cmd)2.5 mmCorrect answer is option 'C'. Can you explain this answer?
Question Description
A paper, with two marks having separation d, isheld normal to the line of sight of an observer ata distance of 50m. The diameter of the eye-lensof the observer is 2 mm. Which of the followingis the least value of d, so that the marks can beseen as separate ? The mean wavelength ofvisible light may be taken as 5000 Å. [2002]a)1.25 mb)13.6 cmc)12.5 cmd)2.5 mmCorrect answer is option 'C'. Can you explain this answer? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about A paper, with two marks having separation d, isheld normal to the line of sight of an observer ata distance of 50m. The diameter of the eye-lensof the observer is 2 mm. Which of the followingis the least value of d, so that the marks can beseen as separate ? The mean wavelength ofvisible light may be taken as 5000 Å. [2002]a)1.25 mb)13.6 cmc)12.5 cmd)2.5 mmCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A paper, with two marks having separation d, isheld normal to the line of sight of an observer ata distance of 50m. The diameter of the eye-lensof the observer is 2 mm. Which of the followingis the least value of d, so that the marks can beseen as separate ? The mean wavelength ofvisible light may be taken as 5000 Å. [2002]a)1.25 mb)13.6 cmc)12.5 cmd)2.5 mmCorrect answer is option 'C'. Can you explain this answer?.
A paper, with two marks having separation d, isheld normal to the line of sight of an observer ata distance of 50m. The diameter of the eye-lensof the observer is 2 mm. Which of the followingis the least value of d, so that the marks can beseen as separate ? The mean wavelength ofvisible light may be taken as 5000 Å. [2002]a)1.25 mb)13.6 cmc)12.5 cmd)2.5 mmCorrect answer is option 'C'. Can you explain this answer? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about A paper, with two marks having separation d, isheld normal to the line of sight of an observer ata distance of 50m. The diameter of the eye-lensof the observer is 2 mm. Which of the followingis the least value of d, so that the marks can beseen as separate ? The mean wavelength ofvisible light may be taken as 5000 Å. [2002]a)1.25 mb)13.6 cmc)12.5 cmd)2.5 mmCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A paper, with two marks having separation d, isheld normal to the line of sight of an observer ata distance of 50m. The diameter of the eye-lensof the observer is 2 mm. Which of the followingis the least value of d, so that the marks can beseen as separate ? The mean wavelength ofvisible light may be taken as 5000 Å. [2002]a)1.25 mb)13.6 cmc)12.5 cmd)2.5 mmCorrect answer is option 'C'. Can you explain this answer?.
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A paper, with two marks having separation d, isheld normal to the line of sight of an observer ata distance of 50m. The diameter of the eye-lensof the observer is 2 mm. Which of the followingis the least value of d, so that the marks can beseen as separate ? The mean wavelength ofvisible light may be taken as 5000 Å. [2002]a)1.25 mb)13.6 cmc)12.5 cmd)2.5 mmCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for A paper, with two marks having separation d, isheld normal to the line of sight of an observer ata distance of 50m. The diameter of the eye-lensof the observer is 2 mm. Which of the followingis the least value of d, so that the marks can beseen as separate ? The mean wavelength ofvisible light may be taken as 5000 Å. [2002]a)1.25 mb)13.6 cmc)12.5 cmd)2.5 mmCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of A paper, with two marks having separation d, isheld normal to the line of sight of an observer ata distance of 50m. The diameter of the eye-lensof the observer is 2 mm. Which of the followingis the least value of d, so that the marks can beseen as separate ? The mean wavelength ofvisible light may be taken as 5000 Å. [2002]a)1.25 mb)13.6 cmc)12.5 cmd)2.5 mmCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A paper, with two marks having separation d, isheld normal to the line of sight of an observer ata distance of 50m. The diameter of the eye-lensof the observer is 2 mm. Which of the followingis the least value of d, so that the marks can beseen as separate ? The mean wavelength ofvisible light may be taken as 5000 Å. [2002]a)1.25 mb)13.6 cmc)12.5 cmd)2.5 mmCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice Class 12 tests.
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