(a) (i) Draw a labelled ray diagram to show the formation of an image in an astronomical telescope for a distant object. (ii) Write three distinct advantages of a reflecting type telescope over a refracting type telescope. (b) A convex lens of focal length 10cm is placed coaxially 5cm away from a concave lens of focal length 10cm. If an object is placed 30cm in front of the convex lens, find the position of the final image formed by the combined system.
Solution
(a)(ii) Reflecting telescope advantages: (1) free from chromatic aberration; (2) large-aperture mirror ⇒ high resolving power and bright image; (3) a parabolic mirror is free from spherical aberration and, supported along its back, does not sag like a large lens. (b) \textbf{Convex lens} (f=+10, u=−30): v1=101−301=302⇒v=+15cm. This image is 15−5=10cm beyond the concave lens, a virtual object u=+10cm. \textbf{Concave lens} (f=−10): v1=f1+u1=−101+101=0⇒v→∞.
