In space, the angular resolution of the Keck telescope is govererned by the diffraction limit.
How far away could you read the same book, using the Keck telescope in space? Please express your answers in units of meters.
Diameter of keck telescope, D= 10m and let Wavelength, λ = 5*10-7 m
θ = Angular diffraction = 1.22(λ/D) = 6.1*10-8
s = r*θ (where θ=6.1*10-8 and s=3*10-3 m)
r= 49180.32 m
Well, if I were to bring the Keck telescope into space to read a book, there might be a few challenges. For one, the pages might get all wrinkly and float away, making it hard to turn them. Plus, without gravity, the bookmark would just drift away, leaving you to endlessly search for your page.
But let's assume we somehow manage to overcome these issues and read the book. The angular resolution of the Keck telescope is determined by the diffraction limit, which depends on factors like the diameter of the telescope aperture and the wavelength of light being used.
The Keck telescope has an aperture diameter of about 10 meters, and let's assume we're using visible light, which has a wavelength of around 500 nanometers. Using some fancy calculations, we find that the diffraction limit for the Keck telescope is roughly 0.02 arcseconds.
Now, let's say our book has pretty small font size, like 10-point font. If we assume each letter takes up about 1 arcminute (1/60th of a degree) on the page, then we can calculate how far away we could read the book.
Using a bit of math magic, we find that the book would need to be approximately 500,000 meters away from the Keck telescope for us to read it with that angular resolution. That's about 310 miles!
Just imagine sitting in space, with a telescope the size of a building, trying to make out tiny letters on a book that's hundreds of miles away. It'd definitely be an interesting sight for any extraterrestrial observers out there!
To determine how far away you could read the same book using the Keck telescope in space, we need to know the angular resolution of the telescope.
The angular resolution of a telescope is determined by the diffraction limit, which is given by the equation:
θ = 1.22 * λ / D
where:
θ is the angular resolution (in radians),
λ is the wavelength of light being observed, and
D is the diameter of the telescope's aperture.
For the Keck telescope, the diameter of the aperture is about 10 meters (D = 10 meters).
Now, let's assume we are observing visible light with a wavelength of about 550 nanometers (λ = 550 * 10^(-9) meters).
Plugging these values into the equation, we can calculate the angular resolution:
θ = 1.22 * (550 * 10^(-9)) / 10
≈ 6.71 * 10^(-8) radians
The angular resolution gives you an idea of how much detail the telescope can discern. To calculate the distance at which you could read the same book using the Keck telescope, we can use the small angle approximation:
distance ≈ height / θ
Assuming a typical book height of about 0.25 meters, we can calculate the distance:
distance ≈ 0.25 / (6.71 * 10^(-8))
≈ 3.73 * 10^6 meters
Therefore, using the Keck telescope in space, you could read the same book from a distance of approximately 3.73 million meters.
To determine how far away you could read the same book using the Keck telescope in space, we need to understand the concept of angular resolution and the diffraction limit.
Angular resolution refers to the smallest angle at which two objects can be distinguished as separate entities. The diffraction limit is a physical phenomenon that sets a fundamental lower limit on the angular resolution of a telescope.
The angular resolution of a telescope is given by the formula:
θ = 1.22 * (λ / D)
where θ represents the angular resolution, λ is the wavelength of light being observed, and D is the diameter of the telescope's aperture.
The Keck telescope has an aperture diameter of 10 meters. Assuming that we are observing light with a wavelength of 550 nanometers (visible light), we can calculate the angular resolution as follows:
θ = 1.22 * (550 nm / 10 m)
Converting the wavelength to meters:
θ = 1.22 * (550 * 10^-9 m / 10 m)
θ = 1.22 * 5.5 * 10^-8
θ = 6.71 * 10^-8 radians
Now that we have the angular resolution, we can calculate the distance at which we can still read the same book. This can be achieved by using basic trigonometry. We can consider the height of the book as the opposite side of a right triangle, and the distance as the adjacent side. The angular resolution θ would then correspond to the angle between these two sides.
Let's assume the height of the book is 0.15 meters. We can rearrange the trigonometry equation as follows:
tan(θ) = height / distance
distance = height / tan(θ)
distance = 0.15 m / tan(6.71 * 10^-8 radians)
Using a calculator, we find:
distance ≈ 2.23 * 10^6 meters
Hence, using the Keck telescope in space, you would be able to read the same book from roughly 2.23 million meters away.