Optical Instruments — Question 9

Question 9

A Galilean telescope uses a virtual object for its negative eyepiece

A telescope objective has fo=30 cm and a diverging eyepiece has fe=-5 cm. A distant object supplies parallel input. Set the lens separation so the output is also parallel.

1. Find the separation by treating the objective focus as the eyepiece virtual object.

2. Find the signed angular magnification using $M=-f_o/f_e$ and compare the length with a positive-eyepiece telescope of the same magnification magnitude.

Question 9 - Solution

A Galilean telescope uses a virtual object for its negative eyepiece

(a) Method and calculation

$$q_o=f_o,\quad p_e=d-f_o,\quad q_e\to\infty\Rightarrow p_e=f_e.$$$$\boxed{d=f_o+f_e=30-5=25\,\mathrm{cm}}.$$

(b) Interpretation and further calculation

$$\boxed{M=-30/(-5)=+6}\quad\text{upright}.$$$$d_{\mathrm{positive}}=30+5=35\,\mathrm{cm}\Rightarrow\boxed{\Delta d=10\,\mathrm{cm}\ \text{shorter}}.$$

Physical check

The negative eyepiece intercepts rays before they reach the objective focus, so its object distance is negative.