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Chapter 5 Problems
2.
6
max
.29cm
1m
10
μ
m
5.5K
100cm
λ
⎛⎞
=×
×
⎜⎟
⎝⎠
, so
max
527
μ
m
=
, which is longer than the 3 to 200
μ
m
operating range.
3.
The amount of light collected by a telescope depends on the area of the mirror, and the area depends
on the
square
of the diameter. A 6m telescope is 3 times bigger in diameter than a 2m telescope, so
it has 3
2
= 9 times the lightgathering power. The larger telescope will gather light 9 times faster than
the smaller telescope, so what the 2m telescope can accomplish in 1 hour, the 6m can accomplish
in 1/9 hour or 6.7 minutes. A 12m telescope has 6 times the diameter of a 2m telescope and
therefore 36 times the area. It gathers light 36 times faster. What the 2m telescope can gather in 1
hour, the 12m can gather in (60 min)/36 = 1.7 minutes.
4.
The angular resolution of a telescope gets poorer as wavelength increases. The angular resolution in
arcseconds is proportional to the wavelength. (a) 3.5
μ
m = 3,500 nm. 3,500/700 = 5, so the
wavelength is 5 times longer. The resolution should be 5 times poorer or 0.05"
×
5 = 0.25".
(b) Similarly, for the ultraviolet, 140 nm/700 nm = 0.2 and 0.05"
×
0.2 = 0.01".
7.
The Hubble Space Telescope has a mirror diameter of 2.4 m. Observing at 400 nm, it can therefore
achieve an angular resolution of 0.25(0.4
μ
m)/(2.4 m) = 0.042". If the stars in the previous problem
have an angular separation of 0.033" at 200 lightyears, then the distance at which their separation
will be 0.042" is (0.033/0.042)(200 lightyears) = 160 lightyears.
9.
Use the last formula in
More Precisely 14
and use arc seconds instead of degrees.
57.3° =
206,000".
Diameter
= 380,000 km(3" / 206,000") = 5.5 km;
Diameter
= 380,000 km(0.05" /
206,000") = 0.092 km = 92 m;
Diameter
= 380,000 km(0.001"/ 206,000”) = 1.8 m.
10.
This is exactly the same problem as the previous problem but with a new distance, 2.5 million light
years.
Diameter
= 2.5 million LY (3"/ 206,000") = 36 Ly; the other two answers are 0.6 Ly and
0.012 Ly ( = 760 A.U.)
11.
The Arecibo telescope is 300 m in diameter.
Comparing the areas of the two telescopes, square their
diameters.
(300)
2
/ (105)
2
= 8.2, so Arecibo collects 8 times more radio waves and is 8 times more
sensitive.
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This note was uploaded on 11/01/2009 for the course PHYS 229 taught by Professor Mehmetyali during the Fall '09 term at Sabancı University.
 Fall '09
 MehmetYali
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