Question

How much more light does an 8-meter telescope gather than a 2-meter telescope?

Answer 1

Answer:

8 meter telescope 16 times more gather light than 2 meter telescope.

Explanation:

The amount of light gather by the telescope is known as Light Gathering Power (LGP).

Light Gathering Power is determine by the relation:

$LGP = \pi \frac{(length\ of\ telescope)^{2} }{4}$

In this problem, let l₁ and l₂ be the length of two telescopes and (LGP)₁ and (LGP)₂ be the light gathering power of two telescopes respectively. Then the ratio of their LGP is :

$\frac{(LGP)_{1} }{(LGP)_{2}} = \frac{l_{1} ^{2} }{l_{2} ^{2}}$

Substitute 8 m for l₁ and 2 m for l₂ in the above equation.

$\frac{(LGP)_{1} }{(LGP)_{2}} = \frac{8 ^{2} }{2 ^{2}}$

$\frac{(LGP)_{1} }{(LGP)_{2}} = 16$