A Cassegrainian telescope uses two mirrors as shown in Fig. Such a telescope is built with the mirrors `20 mm` apart. If the radius of curvature of large mirror is `220 mm` and the small mirror is `40 mm`, where will the final image of an object at infinity be ?

Explanation

The following figure shows a Cassegrain telescope consisting of a concave mirror and a convex mirror.
Distance between the objective mirror and the secondary mirror, d=20mm Radius of curvature of the secondary mirror, R1=140mm
Hence, focal length of the secondary mirror, `f_(2)=R_(2)/2=140/2=70 mm`
The image of an object placed at infity, formed by the objective mirror, will act as a virtual object for the secondary mirror. Hence, the virtual object distance for the secondary mirror, `mu=f_(1)-d`
`110-20 =90mm`
Applying the mirror formula for the secondary mirror, we can calculate image distance (v) as
`1/v+1/u=1/f_(2)`
`1/v=1/f_(2)-1/u`
`-1/70-1/90=(9-7)/(630)=2/630`
`therefore v= 630/2=315mm`
Hence, the final image will be formed 315 mm away from the secondary mirror.