2019年IOAA理论第4题-改进普通的反射望远镜

英文题目

4. Improving a common reflecting telescope (10 p)

A student has an average quality Cassegrain telescope, with primary and secondary mirrors having $$𝜀1 = 91％$$ reflectivity aluminium layers.

a) What will be the change in the limiting magnitude of this telescope by replacing the mirror coatings with "premium" quality $$𝜀2 = 98％$$ reflectivity ones? (5 p)

b) Assuming the student also uses a star diagonal mirror, also with reflectivity 𝜀1 with the original telescope - what will be the improvement if he/she also replaces this piece with an $$𝜀3 = 99％$$ reflectivity (“dielectric” mirror) model, combined with the new $$𝜀2$$ mirrors? (3 p)

(A star diagonal mirror is a flat mirror, inclined to the optical axis by 45°.)

c) Is this difference obviously detectable by the human eye? Mark "YES" or "NO" on the answer sheet. (2 p)

Consider the whole visual band and disregard any wavelength dependence and geometric effects.

中文题目

4. 改进普通反射望远镜(10p)

一个学生有一台普通的卡塞格林望远镜,主镜的副镜镀有反射率$$𝜀1 = 91％$$的铝层。

a)如果用更好的反射率$$𝜀2 = 98％$$换掉镜子，这台望远镜的极限星等会发生什么变化?(5p)

b)假设学生在原来的望远镜上使用斜镜,原始反射率为$$𝜀1$$——- 如果在用新的$$ε2$$的望远镜时，他/她也用$$ε3= 99％$$反射率的斜镜替换这个天顶镜的话，这台望远镜相比于原来将会有什么改进 ？ （3 p）

(斜镜是一种平面镜，倾斜于光轴45°。)

c)这种差异能被人类肉眼明显地检测到吗?在答题纸上的“是”或“否”上作出标记。(2p)

考虑整个视觉波段，忽略任何与波长有关的修正和几何效应。