#2. CCAT is a 25-meter telescope that will detect light with
wavelengths up to 850 microns. How does the angular resolution of this huge
telescope compare to the angular resolution of the much smaller MMT 6.5-meter
telescope observing in the infrared J-band? Ask a TF in class or the internet
about the meaning of “J-band.”
Angular resolution describes how much detail of an image you can resolve. As we learned in class, the angular resolution of telescopes is determined by θmin. Telescopes with a smaller θmin will have a greater resolution. From what Prof Johnson told us in lecture, and from what we worked out Problem 1, θmin=λD with λ being the wavelength of light and D being the diameter of the telescope mirror.
After looking up J-band, we found out that a J-band is a band of light centered at 1.2 microns = 1.2 x 10-4 cm. Also, 850 microns is equivalent to 8.5 x 10-2 cm. Thus, all we had to do was solve for the θmin of each telescope by plugging in the values we already knew.
For the CCAT: θmin=λD θmin=8.5×10−2cm2.5×103cm θmin=3.4×10−5
For the MMT: θmin=λD θmin=1.2×10−4cm6.5×102cm θmin=1.85:×10−7
Thus the MMT, surprisingly, has a better resolution because it has a smaller theta min even though it has a much smaller diameter.
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