IOAA 2019, Теория — Задача 4. Improving a common reflecting telescope
Theory problem sheet · 10 т.
Условие
A student has an average quality Cassegrain telescope, with primary and secondary mirrors having reflectivity aluminium layers.
a) What will be the change in the limiting magnitude of this telescope by replacing the mirror coatings with "premium" quality reflectivity ones? [5 т.]
b) Assuming the student also uses a star diagonal mirror, also with reflectivity with the original telescope - what will be the improvement if he/she also replaces this piece with an reflectivity (“dielectric” mirror) model, combined with the new mirrors?
(A star diagonal mirror is a flat mirror, inclined to the optical axis by .) [3 т.]
c) Is this difference obviously detectable by the human eye? Mark "YES" or "NO" on the answer sheet.
Consider the whole visual band and disregard any wavelength dependence and geometric effects. [2 т.]
Решение
a)
Let us designate the (unknown) original limiting magnitude of this telescope as , and refer to the intensity (at the focal plane) as . The new limiting magnitude is . Due to the additional intensity, which is due to the better reflectivity of the mirror surfaces, the stellar intensity which will result in the same limiting illumination at the focal plane, will be proportionally smaller, with the ratio of the reflectivities of the new and old mirror coatings:
The reflectivities should be multiplied twice, since the light coming from the star, loses some energy twice, suffering reflection on each of the two mirrors.
Now applying the well-known magnitude formula:
With numerical values:
And thus:
b)
Yes, it is well appreciable by most human eyes. Therefore, especially the deep-sky-object hunters are using higher reflectivity mirrors in their telescopes. (2 p)
c)
The similar way of thinking gives:
With numerical values:
And thus:
Оригинал в Архива: TH-problem-final.pdf · официални решения: TH-solution-final.pdf · допълнителни данни: TH-anssheet.pdf