A telescope with a Barlow lens

Adapted from IOAA 2016 (Bhubaneswar), theory problem 7. We have restated it in our own words and kept the original data. The solution was last checked on 20 October 2026.

A refracting telescope of focal ratio f/5 has an objective of focal length 100 cm and an eyepiece of focal length 1 cm.

(1) What is its angular magnification $m_0$, and what is its length $L_0$, the distance from objective to eyepiece? (4 points)

To double the magnification, a Barlow lens of focal length −1 cm is placed between the objective and the focus of the objective.

(2) How far in front of the objective's focus must the Barlow lens be placed? (6 points)

(3) By how much does the telescope become longer? (4 points)

(4) The eyepiece and the Barlow lens are removed, and a camera with pixels 10 µm wide is placed at the objective's focus. How many pixels apart are the images of two stars 20″ apart? (6 points)

AnswerThe telescope magnifies 100 times and is 101 cm long. The Barlow lens goes 0.5 cm in front of the objective's focus, the telescope becomes 0.5 cm longer, and the two stars are about 10 pixels apart on the camera.