(a) (i) Draw a labelled ray diagram to show the formation of 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 10 cm is placed coaxially 5 cm away from a concave lens of focal length 10 cm. If an object is placed 30 cm in front of the convex lens, find the position of the image formed by the combined system.

Explanation

(a) (i) N/A
(ii) (1) Less chromatic aberration. (2) Less spherical aberration. (3) High intense image.
(b) `f_(1)=10` cm, `d=5` cm, `f_(2)=-10` cm, `u=-30` cm, `v=` ?
Combined focal length f is `1/f=1/f_(1)+1/f_(2)-d/(f_(1)f_(2))`
`1/f=1/10+1/(-10)-5/((10)(-10)) implies 1/f=1/10-1/10+5/100 implies f=100/5 =20` cm
Using len's formula, we get `1/f=1/v-1/u`
`1/20=1/v-1/(-30) implies 1/20=1/v+1/30 implies 1/20-1/3-=1/v implies (3-2)/60=1/v`
`:. v=60 cm`.
`:.` Image will be formed at a distance of 60 cm from the combination of lenses.