You want to create a telescope with a resolving power of 0.045 arc seconds at a wavelength of 550 nm. What diameter (in m) do you need? If you want to increase the light gathering power by a factor of 10, by what factor does the diameter need to increase? What would the new resolving power be (in arc seconds)? Part 1 of 5 The resolving power of a telescope is given by

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Chapter1: Units, Trigonometry. And Vectors
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Can you please help with Part 2 of 5?

Part 1 of 5
Astronomy Textbook
You want to create a telescope with a resolving power of 0.045 arc seconds at a wavelength of 550 nm. What diameter (in m) do you need?
If you want to increase the light gathering power by a factor of 10, by what factor does the diameter need to increase?
What would the new resolving power be (in arc seconds)?
Microsoft Office Ho...
The resolving power of a telescope is given by
A
x = 2.06 x 105
(105 금
Part 2 of 5
where both A and D must have the same units.
WebAssign
dameter.
We need to solve this expression for the cameter. You should express your values in meters.
D = 2.06 x 10
D =
0.045 arc seconds
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9
inn
▸
Transcribed Image Text:Part 1 of 5 Astronomy Textbook You want to create a telescope with a resolving power of 0.045 arc seconds at a wavelength of 550 nm. What diameter (in m) do you need? If you want to increase the light gathering power by a factor of 10, by what factor does the diameter need to increase? What would the new resolving power be (in arc seconds)? Microsoft Office Ho... The resolving power of a telescope is given by A x = 2.06 x 105 (105 금 Part 2 of 5 where both A and D must have the same units. WebAssign dameter. We need to solve this expression for the cameter. You should express your values in meters. D = 2.06 x 10 D = 0.045 arc seconds Submit Skip (you cannot come back) 9 inn ▸
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Can you please help with Part 5? Thank you!

Part 4 of 5
If we want to increase the light gathering power by a factor of 10, we need the new telescope to have 10 times the light-gathering power of the original.
10 LGP old
LGP
new
Rearranging the equation for light-gathering power to solve for D new
Plugging in for LGP
D
D new
new
new
= 7.97 ✔
Part 5 of 5
LGP
D new
And using the initial diameter, we can solve for the new diameter.
= 3.16227766017
LGP
new Dold
old
gives:
D
A
3.16 Dold
7.96 m
We can use our new diameter to determine the resolving power of this telescope.
α = 2.06 x 105
arc seconds
M
Transcribed Image Text:Part 4 of 5 If we want to increase the light gathering power by a factor of 10, we need the new telescope to have 10 times the light-gathering power of the original. 10 LGP old LGP new Rearranging the equation for light-gathering power to solve for D new Plugging in for LGP D D new new new = 7.97 ✔ Part 5 of 5 LGP D new And using the initial diameter, we can solve for the new diameter. = 3.16227766017 LGP new Dold old gives: D A 3.16 Dold 7.96 m We can use our new diameter to determine the resolving power of this telescope. α = 2.06 x 105 arc seconds M
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Follow-up Question

Can you help with Part 4?

1
Part 3 of 5
The light gathering power of a telescope depends on the diameter squared.
Part 4 of 5
new
LGP
new
old
D new
If we want to increase the light gathering power by a factor of 10, we need the new telescope to have 10 times the light-gathering power of the original.
LGP
=
D new
Plugging in for LGP
ΠΕΙΝ
D
Rearranging the equation for light-gathering power to solve for D
ΠΕΜΠΤ
old
new
LGP
LGP
Dold
And using the initial diameter, we can solve for the new diameter.
D new
new
LGP old
old
gives:
old
Transcribed Image Text:1 Part 3 of 5 The light gathering power of a telescope depends on the diameter squared. Part 4 of 5 new LGP new old D new If we want to increase the light gathering power by a factor of 10, we need the new telescope to have 10 times the light-gathering power of the original. LGP = D new Plugging in for LGP ΠΕΙΝ D Rearranging the equation for light-gathering power to solve for D ΠΕΜΠΤ old new LGP LGP Dold And using the initial diameter, we can solve for the new diameter. D new new LGP old old gives: old
Solution
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