2016年IOAA理论第7题-望远镜光学结构

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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?

中文翻译

(T7) 望远镜光学结构

在一个焦比为$$f/5$$的理想折射望远镜中，物镜焦距为$$100 \rm{cm}$$，目镜焦距为$$1 \rm{cm}$$。

(T7.1) 望远镜的角度放大倍数$$m_0$$是多少？望远镜的长度，即物镜和目镜之间的距离$$L_0$$是多少？

在物镜和原焦点之间引入凹透镜（巴洛镜）是在不大幅增加望远镜长度的情况下增加放大倍数的常用方法。现在在物镜和目镜之间引入焦距为$$1 \rm{cm}$$的巴洛镜，使放大倍率加倍。

(T7.2) 为了获得所需的双倍放大率，巴洛镜与原焦点的距离$$d_{\rm B}$$是多少？

(T7.3) 望远镜的长度增加值$$\Delta L$$是多少？

现在使用同样的物镜和一个CCD探测器来建造望远镜（不使用巴洛镜或目镜）。CCD探测器的每个像素的尺寸为$$10 \rm{\mu m}$$。

(T7.4) 如果两颗恒星在天空中相距20"，在CCD上的图像质心之间的像素距离$$n_p$$是多少？