Compare the light gathering power of an 8" primary mirror with a 6" primary mirror. The 8" mirror has how much light gathering power?

1.778 times more or 16/9 times more

Step-by-step explanation:

Given:

- Mirror 1: D_1 = 8''

- Mirror 2: D_2 = 6"

Find:

Compare the light gathering power of an 8" primary mirror with a 6" primary mirror. The 8" mirror has how much light gathering power?

Solution:

- The light gathering power of a mirror (LGP) is proportional to the Area of the objects:

LGP ∝ A

- Whereas, Area is proportional to the squared of the diameter i. e an area of a circle:

A ∝ D^2

- Hence, LGP ∝ D^2

- Now compare the two diameters given:

LGP_1 ∝ (D_1) ^2

LGP ∝ (D_2) ^2

- Take a ratio of both:

LGP_1/LGP_2 ∝ (D_1) ^2 / (D_2) ^2

- Plug in the values:

LGP_1/LGP_2 ∝ (8) ^2 / (6) ^2

- Compute: LGP_1/LGP_2 ∝ 16/9 ≅ 1.778 times more