Light-gathering power of a telescope is directly proportional to the area of its primary lens or mirror. All lenses and mirrors have a

circular circumference. The area of a circle is given by the formula: A = 71:72. Because 1: is a constant, the radius, r, of the mirror or lens

is the most important factor in determining the light— gathering power of a telescope. Note that area of a circle varies by the square of the radius. Thus, a lens or mirror that is twice the radius (or diameter) of another telescope objective has 22 or 4 times the light—

gathering power. 1. A typical pair of binoculars has an objective lens of 50-mm diameter. A typical amateur telescope is an 8-inch reﬂector that has a

mirror diameter of 203 mm. (Give answers in a and b as a number; that is, When multiplying, use It as 3.14159.) (a) What is the light-collecting area of the 50-min objective? mm2 [Round to 1 decimal place[

(b) What is the light-collecting area of the 203-mm objective? mm2 [Round to 1 decimal place]

(c) The 203-mm objective collects times the light of a 50-mm objective. [Round to nearest whole number] (d) The brightness of celestial objects usually is expressed in terms of magnitude. A 1St magnitude star is deﬁned as being 100

times brighter than a 6L11 magnitude star (5 magnitude steps). A single magnitude jump equals a brightness change of about

2.512 (given that 2.5125 = 100). Using the factor of 2.5 12 for a single magnitude jump, about how many magnitudes

fainter can the 203-mm objective “see” than the smaller 50-mm objective? [Round to nearest whole number] magnitudes [Hint:2.5121= 2.512; 2.5122 = ?; 2.5123 = ?; 2.5124 = ?; 2.5125 = 100]