Question: 37: An astronomical refracting telescope is being used by an observer to observe planets in normal adjustment. The focal lengths of the objective and eye piece used in the construction of the telescope are 20 m and 2 cm respectively. Consider the following statements about the telescope :
(a) The distance between the objective and eye piece is 20.02 m
(b) The magnification of the telescope is (-) 1000
(c) The image of the planet is erect and diminished
(d) The aperture of eye piece is smaller than that of objective
The correct statements are :
(1) (a), (b) and (c)
(2) (b), (c) and (d)
(3) (c), (d) and (a)
(4) (a), (b) and (d)
Answer: Option (4)
Explanation:
For an astronomical telescope in normal adjustment, the final image is formed at infinity and the distance between the objective and the eyepiece is given by L=f_{o}+f_{e}.
Here, the focal length of the objective is f_{o}=20\,\mathrm{m} and the focal length of the eyepiece is f_{e}=2\,\mathrm{cm}=0.02\,\mathrm{m}.
Therefore, L=20+0.02=20.02\,\mathrm{m}. Hence, statement (a) is correct.
The magnification of an astronomical telescope in normal adjustment is given by
M=-\frac{f_{o}}{f_{e}}.
Substituting the given values, M=-\frac{20}{0.02}=-1000.
The negative sign indicates that the image is inverted.
Hence, statement (b) is correct.
The image formed by an astronomical telescope is inverted and highly magnified, not erect and diminished. Therefore, statement (c) is incorrect.
The objective lens has a large aperture to collect more light from distant objects,
while the eyepiece has a smaller aperture. Hence, statement (d) is correct.
Thus, the correct statements are (a), (b) and (d),
and the correct option is (4).