Resolving Power Practice Questions
1. Complete the missing information in the table using θ = λ/D.
E-M part
Wavelength
Diameter
Ang Res (rad)
Radio
Microwaves
Infra-red
Visible
Ultra-Violet
X-ray
Gamma Ray
0.21m
850 um
72m
50 cm
5m
30.4 nm
0.003 fm
Ang Res
(arcsecs)
508 mm
17m
5.67E-05
4.80E-05
0.022689
0.205589
4.06E-05
2. Estimate the resolving power of the 300m (1000 ft) Arecebo radio dish if it is
operating at a wavelength of 1 metre.
How does this compare with your eye (with a resolution of about 1/60 of a degree or 1
minute of arc)?
Why are radio telescopes so much larger than optical telescopes?
3. Does my 90mm telescope have the resolving power required to split a double star
with an angular separation of 2.2 arc seconds (assume a wavelength of 550 nm)? Why
might it not be possible to observe this double star as two distinct points of light every
night?
4. Calculate the resolving power for a 6 inch and 8 inch telescope observing at optical
wavelengths (estimate the wavelength).
Due to the turbulence of the atmosphere it is very hard to get anything more than 1
arcsecond resolution no matter what size telescope you use.
Why would you therefore use the 8 inch telescope?
5. Two stars are photographed utilising a telescope with a circular aperture of diameter
of 2.46 m and light with a wavelength of 468 nm. If both stars are 1022 m from us,
what is their minimum separation so that we can recognize them as two stars (instead
of just one)?
6. A car passes you on the highway and you notice the taillights of the car are 1.26 m
apart. Assume that the pupils of your eyes have a diameter of 7.1 mm. Given that the
car is 14.4 km away when the tail lights appear to merge into a single spot of light
because of the effects of diffraction, what wavelength of light does the car emit from
its tail lights?
7. Two stars are 5.6 x 1011 m apart and are equally distant from the earth. A telescope
has an objective lens with a diameter of 1.30 m and just detects these stars as separate
objects. Assume that light of wavelength 470 nm is being observed. Also, assume that
diffraction effects, rather than atmospheric turbulence, limit the resolving power of
the telescope. Find the maximum distance that these stars could be from the earth.