When used at a wavelength of 1 micron, a telescope can resolve angles as small as 0.1 seconds of arc. How small an angle could the telescope resolve when used at a wavelength of 5 microns?
a. 0.02 seconds of arc
b. 0.004 seconds of arc
c. 0.5 seconds of arc
d. 0.25 seconds of arc
Arora you're a virgin and everyone knows it.
To find out how small an angle the telescope can resolve when used at a wavelength of 5 microns, we can use the formula:
Resolution = 1.22 * (Wavelength / Diameter)
Given that the telescope can resolve angles as small as 0.1 seconds of arc at a wavelength of 1 micron, we can substitute these values into the formula:
0.1 seconds of arc = 1.22 * (1 micron / Diameter)
Rearranging the equation to solve for the Diameter:
Diameter = 1.22 * (1 micron / 0.1 seconds of arc)
Now, we can calculate the diameter:
Diameter = 1.22 * (1 micron / 0.1 seconds of arc)
Diameter = 1.22 * (1 micron / 0.1)
Diameter = 1.22 * 10 microns
Diameter = 12.2 microns
Now, we can calculate the resolution when used at a wavelength of 5 microns by substituting 5 microns into the formula:
Resolution = 1.22 * (5 microns / Diameter)
Resolution = 1.22 * (5 microns / 12.2 microns)
Resolution = 1.22 * 0.41
Resolution ≈ 0.50 seconds of arc
Therefore, the telescope can resolve angles as small as approximately 0.50 seconds of arc when used at a wavelength of 5 microns.
Therefore, the correct answer is c. 0.5 seconds of arc.
To understand how to solve this problem, we need to use the concept of angular resolution. The formula for calculating angular resolution is given by:
θ = 1.22 * λ / D
Where:
θ is the angular resolution
λ is the wavelength of light used
D is the diameter of the telescope's aperture
Given that the telescope can resolve angles as small as 0.1 seconds of arc when used at a wavelength of 1 micron, we can plug these values into the formula and solve for D:
0.1 = 1.22 * 1 / D
Simplifying the equation:
0.1D = 1.22
D = 1.22 / 0.1
D = 12.2 microns
Now, we can use the calculated diameter of the telescope's aperture to determine the angular resolution when used at a wavelength of 5 microns. Plugging the values into the formula:
θ = 1.22 * 5 / 12.2
Simplifying the equation:
θ = 6.1 / 12.2
θ ≈ 0.5 seconds of arc
Therefore, the telescope can resolve angles as small as 0.5 seconds of arc when used at a wavelength of 5 microns. So the answer is option c.
Having answered half of your many question, I'd like to see what thoughts you have on these questions before posting any further solutions.
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