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

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

University Physics Volume 2

18th Edition

ISBN:9781938168161

Author:OpenStax

Publisher:OpenStax

Chapter16: Electromagnetic Waves

Section: Chapter Questions

Problem 14CQ: Why did the early Hubble Telescope photos of Cornet Ison approaching Earth show it to have merely a...

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Question

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
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

Solution

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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

Solution

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