2016年IOAA理论第7题-望远镜光学结构

英文题目

(T7) Telescope optics

In a particular ideal refracting telescope of focal ratio 𝑓/5, the focal length of the objective lens is 100 cm and that of the eyepiece is 1 cm.

(T7.1) What is the angular magnification, 𝑚₀ , of the telescope? What is the length of the telescope, 𝐿₀ , i.e. the distance between its objective and eyepiece?

An introduction of a concave lens (Barlow lens) between the objective lens and the prime focus is a common way to increase the magnification without a large increase in the length of the telescope. A Barlow lens of focal length 1 cm is now introduced between the objective and the eyepiece to double the magnification.

(T7.2) At what distance, 𝑑_B, from the prime focus must the Barlow lens be kept in order to obtain this desired double magnification?

(T7.3) What is the increase, Δ𝐿, in the length of the telescope?

A telescope is now constructed with the same objective lens and a CCD detector placed at the prime focus (without any Barlow lens or eyepiece). The size of each pixel of the CCD detector is 10 µm.

(T7.4) What will be the distance in pixels between the centroids of the images of the two stars , 𝑛_p , on the CCD, if they are 20′′ apart on the sky?