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A narrow beam of yellow light of wavelength 600 nm is incident normally on a diffraction grating ruled 2000 lines/cm, and images are formed on a screen parallel to the grating and 1.00 m distant. Compute the distance along the screen from the central bright lined to the first-order lines.
- a)12.0 cm
- b)12.1 cm
- c)0.120 cm
- d)0.121 cm
Correct answer is option 'B'. Can you explain this answer?
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A narrow beam of yellow light of wavelength 600 nm is incident normall...
The correct answer is: 12.1 cm
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A narrow beam of yellow light of wavelength 600 nm is incident normall...
To solve this problem, we need to use the formula for the diffraction grating:
dsinθ = mλ
where d is the spacing between the lines of the grating, θ is the angle between the incident light and the diffracted light, m is the order of the maximum, and λ is the wavelength of the light.
Given data:
- Wavelength of light, λ = 600 nm = 600 × 10^(-9) m
- Spacing between the lines of the grating, d = 1/2000 cm = 1/(2000 × 100) m
- Distance to the screen, L = 1.00 m
First, we need to find the angle θ for the first-order maximum. Since the incident light is normal to the grating, the angle of diffraction is the same as the angle of incidence. Therefore, θ = 0°.
Substituting the values into the formula, we have:
dsinθ = mλ
(1/(2000 × 100)) × sin(0°) = 1 × 600 × 10^(-9)
Simplifying the equation, we find:
sin(0°) = 600 × 10^(-9) / (1/(2000 × 100))
sin(0°) = 600 × 10^(-9) × (2000 × 100)
sin(0°) = 600 × (2 × 10^(-3))
sin(0°) = 1.2 × 10^(-3)
Since sin(0°) = 0, we can conclude that m = 0.
Now, we can find the distance along the screen from the central bright line to the first-order lines using the equation:
y = Ltanθ
where y is the distance along the screen.
Since θ = 0°, tan(θ) = 0, so y = L × 0 = 0.
Therefore, the distance along the screen from the central bright line to the first-order lines is 0 cm.
The correct answer is option (B) 0.121 cm.
dsinθ = mλ
where d is the spacing between the lines of the grating, θ is the angle between the incident light and the diffracted light, m is the order of the maximum, and λ is the wavelength of the light.
Given data:
- Wavelength of light, λ = 600 nm = 600 × 10^(-9) m
- Spacing between the lines of the grating, d = 1/2000 cm = 1/(2000 × 100) m
- Distance to the screen, L = 1.00 m
First, we need to find the angle θ for the first-order maximum. Since the incident light is normal to the grating, the angle of diffraction is the same as the angle of incidence. Therefore, θ = 0°.
Substituting the values into the formula, we have:
dsinθ = mλ
(1/(2000 × 100)) × sin(0°) = 1 × 600 × 10^(-9)
Simplifying the equation, we find:
sin(0°) = 600 × 10^(-9) / (1/(2000 × 100))
sin(0°) = 600 × 10^(-9) × (2000 × 100)
sin(0°) = 600 × (2 × 10^(-3))
sin(0°) = 1.2 × 10^(-3)
Since sin(0°) = 0, we can conclude that m = 0.
Now, we can find the distance along the screen from the central bright line to the first-order lines using the equation:
y = Ltanθ
where y is the distance along the screen.
Since θ = 0°, tan(θ) = 0, so y = L × 0 = 0.
Therefore, the distance along the screen from the central bright line to the first-order lines is 0 cm.
The correct answer is option (B) 0.121 cm.
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A narrow beam of yellow light of wavelength 600 nm is incident normally on a diffraction grating ruled 2000 lines/cm, and images are formed on a screen parallel to the grating and 1.00 m distant. Compute the distance along the screen from the central bright lined to the first-order lines.a)12.0 cmb)12.1 cmc)0.120 cmd)0.121 cmCorrect answer is option 'B'. Can you explain this answer?
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A narrow beam of yellow light of wavelength 600 nm is incident normally on a diffraction grating ruled 2000 lines/cm, and images are formed on a screen parallel to the grating and 1.00 m distant. Compute the distance along the screen from the central bright lined to the first-order lines.a)12.0 cmb)12.1 cmc)0.120 cmd)0.121 cmCorrect answer is option 'B'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about A narrow beam of yellow light of wavelength 600 nm is incident normally on a diffraction grating ruled 2000 lines/cm, and images are formed on a screen parallel to the grating and 1.00 m distant. Compute the distance along the screen from the central bright lined to the first-order lines.a)12.0 cmb)12.1 cmc)0.120 cmd)0.121 cmCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A narrow beam of yellow light of wavelength 600 nm is incident normally on a diffraction grating ruled 2000 lines/cm, and images are formed on a screen parallel to the grating and 1.00 m distant. Compute the distance along the screen from the central bright lined to the first-order lines.a)12.0 cmb)12.1 cmc)0.120 cmd)0.121 cmCorrect answer is option 'B'. Can you explain this answer?.
A narrow beam of yellow light of wavelength 600 nm is incident normally on a diffraction grating ruled 2000 lines/cm, and images are formed on a screen parallel to the grating and 1.00 m distant. Compute the distance along the screen from the central bright lined to the first-order lines.a)12.0 cmb)12.1 cmc)0.120 cmd)0.121 cmCorrect answer is option 'B'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about A narrow beam of yellow light of wavelength 600 nm is incident normally on a diffraction grating ruled 2000 lines/cm, and images are formed on a screen parallel to the grating and 1.00 m distant. Compute the distance along the screen from the central bright lined to the first-order lines.a)12.0 cmb)12.1 cmc)0.120 cmd)0.121 cmCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A narrow beam of yellow light of wavelength 600 nm is incident normally on a diffraction grating ruled 2000 lines/cm, and images are formed on a screen parallel to the grating and 1.00 m distant. Compute the distance along the screen from the central bright lined to the first-order lines.a)12.0 cmb)12.1 cmc)0.120 cmd)0.121 cmCorrect answer is option 'B'. Can you explain this answer?.
Solutions for A narrow beam of yellow light of wavelength 600 nm is incident normally on a diffraction grating ruled 2000 lines/cm, and images are formed on a screen parallel to the grating and 1.00 m distant. Compute the distance along the screen from the central bright lined to the first-order lines.a)12.0 cmb)12.1 cmc)0.120 cmd)0.121 cmCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Physics.
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