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A diffraction grating spectrograph is used to resolve the two sodium D lines (589 nm and 589.6 nm) in the first order of diffraction. If the width of the grating is 2cm and the focal length of the spectrograph camera is 20 cm, what the linear separation at the focal plane of the two D lines will be about (a) 6 um (b) 6mm (c) 60 μm (d) 60 nm?
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A diffraction grating spectrograph is used to resolve the two sodium D...
Given:
- Width of the grating = 2 cm
- Focal length of the spectrograph camera = 20 cm
- Wavelengths of the sodium D lines = 589 nm and 589.6 nm
To find:
The linear separation at the focal plane of the two D lines
Concept:
Diffraction grating is an optical device that consists of a large number of equally spaced parallel slits. It is used to disperse light into its component wavelengths. The angle of diffraction for a particular wavelength can be determined using the grating equation:
sinθ = mλ/d
where:
- θ is the angle of diffraction
- m is the order of diffraction
- λ is the wavelength of light
- d is the spacing between the slits
In the first order of diffraction (m = 1), the angle of diffraction for the two sodium D lines can be calculated using the above equation. The linear separation at the focal plane can be determined by multiplying the angular separation by the focal length of the spectrograph camera.
Calculation:
1. Calculate the angle of diffraction for the two sodium D lines:
- For λ = 589 nm:
sinθ₁ = (1 * 589 nm) / (2 cm)
sinθ₁ = 0.589 nm / 2 cm
θ₁ = sin⁻¹(0.589 nm / 2 cm)
- For λ = 589.6 nm:
sinθ₂ = (1 * 589.6 nm) / (2 cm)
sinθ₂ = 0.5896 nm / 2 cm
θ₂ = sin⁻¹(0.5896 nm / 2 cm)
2. Calculate the angular separation between the two D lines:
Δθ = θ₂ - θ₁
3. Calculate the linear separation at the focal plane:
Linear separation = Δθ * focal length
Answer:
The linear separation at the focal plane of the two sodium D lines will be approximately 60 μm (option c).
- Width of the grating = 2 cm
- Focal length of the spectrograph camera = 20 cm
- Wavelengths of the sodium D lines = 589 nm and 589.6 nm
To find:
The linear separation at the focal plane of the two D lines
Concept:
Diffraction grating is an optical device that consists of a large number of equally spaced parallel slits. It is used to disperse light into its component wavelengths. The angle of diffraction for a particular wavelength can be determined using the grating equation:
sinθ = mλ/d
where:
- θ is the angle of diffraction
- m is the order of diffraction
- λ is the wavelength of light
- d is the spacing between the slits
In the first order of diffraction (m = 1), the angle of diffraction for the two sodium D lines can be calculated using the above equation. The linear separation at the focal plane can be determined by multiplying the angular separation by the focal length of the spectrograph camera.
Calculation:
1. Calculate the angle of diffraction for the two sodium D lines:
- For λ = 589 nm:
sinθ₁ = (1 * 589 nm) / (2 cm)
sinθ₁ = 0.589 nm / 2 cm
θ₁ = sin⁻¹(0.589 nm / 2 cm)
- For λ = 589.6 nm:
sinθ₂ = (1 * 589.6 nm) / (2 cm)
sinθ₂ = 0.5896 nm / 2 cm
θ₂ = sin⁻¹(0.5896 nm / 2 cm)
2. Calculate the angular separation between the two D lines:
Δθ = θ₂ - θ₁
3. Calculate the linear separation at the focal plane:
Linear separation = Δθ * focal length
Answer:
The linear separation at the focal plane of the two sodium D lines will be approximately 60 μm (option c).
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A diffraction grating spectrograph is used to resolve the two sodium D lines (589 nm and 589.6 nm) in the first order of diffraction. If the width of the grating is 2cm and the focal length of the spectrograph camera is 20 cm, what the linear separation at the focal plane of the two D lines will be about (a) 6 um (b) 6mm (c) 60 μm (d) 60 nm?
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A diffraction grating spectrograph is used to resolve the two sodium D lines (589 nm and 589.6 nm) in the first order of diffraction. If the width of the grating is 2cm and the focal length of the spectrograph camera is 20 cm, what the linear separation at the focal plane of the two D lines will be about (a) 6 um (b) 6mm (c) 60 μm (d) 60 nm? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about A diffraction grating spectrograph is used to resolve the two sodium D lines (589 nm and 589.6 nm) in the first order of diffraction. If the width of the grating is 2cm and the focal length of the spectrograph camera is 20 cm, what the linear separation at the focal plane of the two D lines will be about (a) 6 um (b) 6mm (c) 60 μm (d) 60 nm? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A diffraction grating spectrograph is used to resolve the two sodium D lines (589 nm and 589.6 nm) in the first order of diffraction. If the width of the grating is 2cm and the focal length of the spectrograph camera is 20 cm, what the linear separation at the focal plane of the two D lines will be about (a) 6 um (b) 6mm (c) 60 μm (d) 60 nm?.
A diffraction grating spectrograph is used to resolve the two sodium D lines (589 nm and 589.6 nm) in the first order of diffraction. If the width of the grating is 2cm and the focal length of the spectrograph camera is 20 cm, what the linear separation at the focal plane of the two D lines will be about (a) 6 um (b) 6mm (c) 60 μm (d) 60 nm? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about A diffraction grating spectrograph is used to resolve the two sodium D lines (589 nm and 589.6 nm) in the first order of diffraction. If the width of the grating is 2cm and the focal length of the spectrograph camera is 20 cm, what the linear separation at the focal plane of the two D lines will be about (a) 6 um (b) 6mm (c) 60 μm (d) 60 nm? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A diffraction grating spectrograph is used to resolve the two sodium D lines (589 nm and 589.6 nm) in the first order of diffraction. If the width of the grating is 2cm and the focal length of the spectrograph camera is 20 cm, what the linear separation at the focal plane of the two D lines will be about (a) 6 um (b) 6mm (c) 60 μm (d) 60 nm?.
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A diffraction grating spectrograph is used to resolve the two sodium D lines (589 nm and 589.6 nm) in the first order of diffraction. If the width of the grating is 2cm and the focal length of the spectrograph camera is 20 cm, what the linear separation at the focal plane of the two D lines will be about (a) 6 um (b) 6mm (c) 60 μm (d) 60 nm?, a detailed solution for A diffraction grating spectrograph is used to resolve the two sodium D lines (589 nm and 589.6 nm) in the first order of diffraction. If the width of the grating is 2cm and the focal length of the spectrograph camera is 20 cm, what the linear separation at the focal plane of the two D lines will be about (a) 6 um (b) 6mm (c) 60 μm (d) 60 nm? has been provided alongside types of A diffraction grating spectrograph is used to resolve the two sodium D lines (589 nm and 589.6 nm) in the first order of diffraction. If the width of the grating is 2cm and the focal length of the spectrograph camera is 20 cm, what the linear separation at the focal plane of the two D lines will be about (a) 6 um (b) 6mm (c) 60 μm (d) 60 nm? theory, EduRev gives you an
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