Question

A Cassegrain telescope uses two mirrors as shown in Fig. 9.33. Sucha telescope is built with the mirrors 20mm apart. If the radius ofcurvature of the large mirror is 220 mm and the small mirror is 140mm, where will the final image of an object at infinity be?

Answer 1

Given,

Distance between objective mirror and secondary mirror d=20 mm.

Radius of curvature of the large mirror or objective mirror, R 1 =220 mm.

Radius of curvature of the small mirror, R 2 =140 mm

Since, R 1 =220 mm

Thus, focal length of the large mirror

f 1 = R 1 2 = 220 2 =110 mm

Since, R 2 =140 mm

Thus, the focal length of the small mirror is

f 2 = 140 2 =70 mm

The image of an object placed at infinity, formed by the objective mirror will act as a virtual object for the small mirror.

Thus, the object distance for small mirror will be,

u= f 1 −d =110−20 =90 mm

Apply the mirror formula,

1 v = 1 f 2 − 1 u = 1 70 − 1 90 = 1 315

Thus, v=315 mm

Thus, the image will be formed at a distance 315 mmaway from the small mirror.