The Hale Telescope has a mirror of diameter 5.1 meters and a focal length of 16.9 meters. The Keck 1 Telescope has a mirror of diameter 10 meters and a focal length of 17.5 meters. Which telescope has a greater light-gathering power (i.e., can collect more photons per second)?
since the only light the telescope can gather has to come in through the lens, the larger diameter can gather more light.
The focal length is related to the magnification.
google can provide you with further discussions on these topics.
Ah, telescopes! They do love to gather light and play cosmic games. Well, let's see here. The Hale Telescope boasts a mirror with a diameter of 5.1 meters and a focal length of 16.9 meters. On the other hand, the Keck 1 Telescope showcases a mirror with a diameter twice as large, measuring 10 meters, and a focal length of 17.5 meters. Now, when it comes to light-gathering power, it ultimately depends on the size of the mirror since that's where the real party happens. In this case, the Keck 1 Telescope definitely takes the cake, or should I say, the photons! With its gargantuan 10-meter-diameter mirror, it will outshine the Hale Telescope any day, collecting more photons per second to impress the cosmic audiences. It's like having a larger spoon to scoop up more ice cream—more heavenly goodness for the Keck 1 is guaranteed!
To determine which telescope has a greater light-gathering power, we can compare their light-collecting areas. The light-collecting area is proportional to the square of the diameter of the mirror.
For the Hale Telescope:
Mirror diameter = 5.1 meters
Light-collecting area = (5.1 meters)^2 = 26.01 square meters
For the Keck 1 Telescope:
Mirror diameter = 10 meters
Light-collecting area = (10 meters)^2 = 100 square meters
Comparing the light-collecting areas of the two telescopes, we can see that the Keck 1 Telescope has a larger light-collecting area. Therefore, the Keck 1 Telescope has a greater light-gathering power and can collect more photons per second.
To determine which telescope has greater light-gathering power, we need to calculate the light-gathering area of each telescope. The light-gathering area is proportional to the square of the diameter of the telescope's mirror.
Let's calculate the light-gathering area for each telescope:
For the Hale Telescope:
Diameter = 5.1 meters
Radius = Diameter / 2 = 5.1 / 2 = 2.55 meters
Light-gathering area = π * r^2 = π * (2.55)^2 ≈ 20.41 square meters
For the Keck 1 Telescope:
Diameter = 10 meters
Radius = Diameter / 2 = 10 / 2 = 5 meters
Light-gathering area = π * r^2 = π * (5)^2 ≈ 78.54 square meters
Now, we can compare the light-gathering areas of the two telescopes. The Keck 1 Telescope has a significantly larger light-gathering area (78.54 square meters) compared to the Hale Telescope (20.41 square meters).
Therefore, the Keck 1 Telescope has greater light-gathering power and can collect more photons per second.