Compare the light gathering power of a telescope with a 10-centimeter(about 4-inch) diameter mirror to that of the human eye. (Take a diameter of the pupil of the eye to be about 5 millimeters)
Wouldn't the power be related to the AREA of the optical window in the telescope?
Yes, you are correct. The light gathering power of a telescope is indeed related to the area of its optical window. The larger the diameter of the telescope's mirror or lens, the more light it can gather.
To compare the light gathering power of the telescope with a 10-centimeter diameter mirror to that of the human eye, we need to calculate the areas of their respective optical windows.
Step 1: Calculate the area of the telescope's optical window.
A = π * (r)^2
= π * (5 cm)^2
≈ 78.54 cm^2
Step 2: Calculate the area of the human eye's optical window.
A = π * (r)^2
= π * (0.5 cm)^2
≈ 0.79 cm^2
So, the area of the telescope's optical window is approximately 78.54 cm^2, while the area of the human eye's optical window is approximately 0.79 cm^2.
This means that the telescope's light gathering power is roughly 100 times greater than that of the human eye (78.54 cm^2 divided by 0.79 cm^2).