2. Compare an amateur telescope of 100 mm (a typical "4-inch" telescope, usually a refractor) with that of the Keck telescope,

which is 10 meters across. [Hint: Work in powers often; "2 decimals" means after the decimal point in powers of ten notation.]

(a) Area of 100-mm objective in mm:

mm [Write in scientific notation and round to 2 decimals; same for part b]

(b) Area of 100-mm objective in m':

m' (Careful! Note the conversion from millimeters to meters. Working

with powers of ten can make this step easier. Hint: How many mm in 1 meter? How many mm in 1 m ?) [Round to 2 decimals]

(c) Area of 10-m Keck objective:

m [Write answer in scientific notation and round to 2 decimals]

(d) 10-m objective collects

times the light of a 100-mm objective [Round to nearest whole number]

(e) The answer to (d) represents how many magnitudes?

(Hint: Look for the x" function on a scientific calculator. If (2.512) = 100 and represents 5 magnitude steps, then how

many steps does the answer to d represent? If 100 = 10 x 10 or 102, then how many powers of ten is the answer to d?)

3. A quicker way to calculate light-gathering power is to use the formula:

LGP

LGP

D.

[ Hint: Don't forget that on the right side the values are squared after being divided.]

where LGPA and LGPe are the light-gathering powers of A and B, respectively, and DA and De are the diameters of objectives A

and B. respectively. If the human eye has a diameter of 8 mm (actually the pupil of the eye), and we have both a 50-mm telescope

and a 203-mm telescope, how much more light will the telescopes gather than our eye? [Round answers to nearest whole number]

(a) LGPsom/LGPeye =

times more light

(b) LGP20 mm/LGPye =

times more light