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A Cassegrain telescope uses two mirrors as shown in Fig. 9.10. Such a telescope is built with the mirrors 20 mm apart. If the radius of curvature of the large mirror is 220 mm and the small mirror is 140 mm, where will the final image of an object at infinity be ? |
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Answer» Solution :Radius of curvature of LARGER mirror `R_(1) = 220 mm = 22 cm` and hence, its focal length `f_(1) = 11 cm`For an object situated at `infty`,this mirror may focus, in the absence of smaller mirror, at a distance 11 cm from it. This image will behave as a virtual object for the smaller convex mirror. `therefore` For smaller mirror `f_(2) =R_(2)/2 = (140 mm)/2 = 70 mm = 7 cm` As distance between the two MIRRORS`x= 20 mm = 2cm` As `1/v_(2) + 1/u_(2) = 1/f_(2)` and `u_(2)` and `f_(2)` both are postiive, hence, `1/v_(2) = 1/f_(2) -1/u_(2) =1/7 - 1/9 rArr v_(2) = 31.5 cm = 315 mm` Thus, the final image is at a distance of 31.5 cm from the smaller mirror (or 29.5 cm BEHIND the bigger mirror). |
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