Geometrical OpticsHard
Question
An astronomical telescope has an angular magnification of magnitude 5 for far bjects. The separation between the objective and the eyepiece is 36 cm and the final image is formed at infinity. The focal length f0 of the objective and focal length fe of the eyepiece are
Options
A.f0 = 45 cm and fe = - 9 cm
B.f0 = 50 cm and fe = 10 cm
C.f0 = 7.2 cm and fe = 5 cm
D.f0 = 30 cm and fe = 6 cm
Solution
Image formed by objective (I1) is at second focus of it because objective is focussed for diatnce objects. Therefore,
P1I1 = f0
Further I1 should lie at first focus of eyepiece because final image is formed at infinity.
∴ P2I1 = f2
Given P1I2 = 36
∴ f0 + fe = 36 .....(i)
Further angular magnification is given as 5. Therefore,
.....(ii)Solving Eqs. (i) and (ii), we get
f0 = 30 cm and fe = 6 cm.
∴ Correct option is (d).
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