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.