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Rowan Introduction to AstronomyLab 5 / Properties of Telescopes: Light-GatheringPower, Magnification, ResolutionName:________________________________________________Score:__________________________Summary:The student will learn about the relationship between objective size, resolution, focal length, and magnification..Light-Gathering Power[33 pts]Light-gathering power of a telescope is directly proportional to the area of its primary lens or mirror. All lenses and mirrors have acircular circumference. The area of a circle is given by the formula:A= πr2. Because π is a constant, the radius,r,of the mirror or lensis the most important factor in determining the light-gathering power of a telescope. Note that area of a circle varies by the square ofthe radius. Thus, a lens or mirror that is twice the radius (or diameter) of another telescope objective has 22or 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 amirror diameter of 203 mm. (Give answers inaandbas a number; that is, when multiplying, useπ as 3.14159.)(a)What is the light-collecting area of the 50-mm objective? _________________________ mm2[Round to1decimal place](b) What is the light-collecting area of the 203-mm objective? _________________________ mm2[Round to1decimal place](c)The 203-mm objective collects _______________ times the light of a 50-mm objective.[Round tonearestwhole number](d) The brightness of celestial objects usually is expressed in terms of magnitude. A 1stmagnitude star is defined as being 100times brighter than a 6thmagnitude star (5 magnitude steps). A single magnitude jump equals a brightness change of about2.512 (given that 2.5125= 100). Using the factor of 2.512 for a single magnitude jump, about how many magnitudesfainter 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]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 of ten; “2 decimals” means after the decimal point in powers of ten notation.]
(a)Area of 100-mm objective in mm2: _______________ mm2[Write in scientific notation and round to2decimals; same for partb](b)Area of 100-mm objective in m2: _______________ m2(Careful! Note the conversion from millimeters2to meters2. Workingwith powers of ten can make this step easier. Hint: How many mm in 1 meter? How many mm2in 1 m2?)[Round to2decimals]