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What wavelength of light would you be able to resolve at the furthest distance based on diffraction?
- a)Green λ = 550 nm
- b)Blue λ = 450 nm
- c)all wavelengths will be resolved equally
- d)Red λ = 650 nm
Correct answer is option 'B'. Can you explain this answer?
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What wavelength of light would you be able to resolve at the furthest ...
∴ Blue light (A = 450 nm)
The correct answer is: Blue λ = 450 nm
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What wavelength of light would you be able to resolve at the furthest ...
Green light has a wavelength of approximately 555 nanometers (nm).
To calculate the minimum resolvable distance based on diffraction, we can use the formula:
θ ≈ 1.22 * (λ / D)
Where:
θ = angular resolution (in radians)
λ = wavelength of light (in meters)
D = diameter of the aperture (in meters)
Assuming we have a telescope with an aperture of 1 meter, we can substitute the values into the formula:
θ ≈ 1.22 * (555 nm / 1 m)
Converting the wavelength to meters:
θ ≈ 1.22 * (555 * 10^-9 m / 1 m)
Simplifying:
θ ≈ 1.22 * 5.55 * 10^-7 radians
θ ≈ 6.77 * 10^-7 radians
To find the minimum resolvable distance (d), we can use the formula:
d = R * θ
Where:
d = minimum resolvable distance (in meters)
R = distance between the observer and the object (in meters)
Assuming we are observing an object at a distance of 1 light year (approximately 9.461 × 10^15 meters):
d ≈ (9.461 × 10^15 m) * (6.77 * 10^-7 radians)
Simplifying:
d ≈ 6.398 × 10^9 meters
Therefore, based on diffraction, you would be able to resolve a wavelength of green light at a distance of approximately 6.398 billion meters (or 6.398 million kilometers) using a 1-meter aperture telescope.
To calculate the minimum resolvable distance based on diffraction, we can use the formula:
θ ≈ 1.22 * (λ / D)
Where:
θ = angular resolution (in radians)
λ = wavelength of light (in meters)
D = diameter of the aperture (in meters)
Assuming we have a telescope with an aperture of 1 meter, we can substitute the values into the formula:
θ ≈ 1.22 * (555 nm / 1 m)
Converting the wavelength to meters:
θ ≈ 1.22 * (555 * 10^-9 m / 1 m)
Simplifying:
θ ≈ 1.22 * 5.55 * 10^-7 radians
θ ≈ 6.77 * 10^-7 radians
To find the minimum resolvable distance (d), we can use the formula:
d = R * θ
Where:
d = minimum resolvable distance (in meters)
R = distance between the observer and the object (in meters)
Assuming we are observing an object at a distance of 1 light year (approximately 9.461 × 10^15 meters):
d ≈ (9.461 × 10^15 m) * (6.77 * 10^-7 radians)
Simplifying:
d ≈ 6.398 × 10^9 meters
Therefore, based on diffraction, you would be able to resolve a wavelength of green light at a distance of approximately 6.398 billion meters (or 6.398 million kilometers) using a 1-meter aperture telescope.
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What wavelength of light would you be able to resolve at the furthest distance based on diffraction?a)Greenλ= 550 nmb)Blueλ= 450 nmc)all wavelengths will be resolved equallyd)Redλ =650 nmCorrect answer is option 'B'. Can you explain this answer?
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