(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)
(ii) First, there is no chromatic aberration in a mirror. Second, if a parabolic reflecting suface is chosen, spherical aberration in also removed. Mechanical support is much less of a problem since a mirror weighs much less than a lens of equivalent optical quality, and can be supported over its entire back surface, not just over its rim.
(b) `f_(1)=10 cm, d=5 cm, f_(2)=-10 cm`
`u=-30 cm, v=?`
Combined focal length `f` is
`(1)/(f)=I(1)/(f_(1))+(1)/(f_(2))-(d)/(f_(1)f_(2)), (1)/(f)=(1)/(10)+(1)/(-10)-(5)/((10)(-10))`
`(1)/(f)=(1)/(10)-(1)/(10)+(5)/(100) rArr f=(100)/(5)=20 cm`
`(1)/(f)=(1)/(v)-(1)/(u), (1)/(20)=(1)/(v)-(1)/(-30)rArr(1)/(20)=(1)/(v)+(1)/(30)`
`(1)/(20)-(1)/(30)=(1)/(v)rArr(3-2)/(60)=(1)/(v)`
`therefore v=60 cm`
`therefore` Image will be formed at a distance of `30 cm` from the combination of lenses.