Lab 5 / Properties of Telescopes: Light-Gathering
Power, Magnification, Resolution
Name: ________________________________________________ Score: __________________________
ySummary: The student will learn about the relationship between objective size, resolution, focal length, and magnification..
yLight-Gathering Power [33 pts]
Light-gathering power of a telescope is directly propor
...[Show More]
Lab 5 / Properties of Telescopes: Light-Gathering
Power, Magnification, Resolution
Name: ________________________________________________ Score: __________________________
ySummary: The student will learn about the relationship between objective size, resolution, focal length, and magnification..
yLight-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 = πr2. 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 22 or 4 times the lightgathering 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? _________________________ 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 6th 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 2.512 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: 2.5121 = 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 to 2 decimals; same for part b]
(b) Area of 100-mm objective in m2: _______________ m2 (Careful! Note the conversion from millimeters2 to meters2. Working
with powers of ten can make this step easier. Hint: How many mm in 1 meter? How many mm2 in 1 m2?) [Round to 2 decimals]
(c) Area of 10-m Keck objective: ____________________ m2 [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 xy 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 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:
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