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what is the light-collecting area of the 50-mm objective?____ mm2?

what is the light-collecting area of the 203-mm objective?___mm2?

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Rowan Introduction to Astronomy Lab 5 / Properties of Telescopes: Light-Gathering Power, Magnification, Resolution Name: ________________________________________________ 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 a circular circumference. The area of a circle is given by the formula: A = π r 2 . Because π 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 2 2 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 π as 3.14159.) (a) What is the light-collecting area of the 50-mm objective? _________________________ mm 2 [Round to 1 decimal place] (b) What is the light-collecting area of the 203-mm objective? _________________________ mm 2 [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 1 st magnitude star is defined as being 100 times brighter than a 6 th magnitude star (5 magnitude steps). A single magnitude jump equals a brightness change of about 2.512 (given that 2.512 5 = 100). Using the factor of 2.512 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: 2.512 1 = 2.512; 2.512 2 = ?; 2.512 3 = ?; 2.512 4 = ?; 2.512 5 = 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 mm 2 : _______________ mm 2 [Write in scientific notation and round to 2 decimals; same for part b ] (b) Area of 100-mm objective in m 2 : _______________ m 2 (Careful! Note the conversion from millimeters 2 to meters 2 . Working with powers of ten can make this step easier. Hint: How many mm in 1 meter? How many mm 2 in 1 m 2 ?) [Round to 2 decimals] (c) Area of 10-m Keck objective: ____________________ m 2 [ 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 y function on a scientific calculator. If (2.512) 5 = 100 and represents 5 magnitude steps, then how many steps does the answer to d represent? If 100 = 10 × 10 or 10 2 , 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: 2 B A B A D D LGP LGP [Hint: Don’t forget that on the right side the values are squared after being divided.] where LGP A and LGP B are the light-gathering powers of A and B, respectively, and D A and D B 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) LGP 50mm / LGP eye = _______________ times more light (b) LGP 203mm / LGP eye = _______________ times more light
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