An astronomical telescope has an angular magnification of magnitude `5` for distant object. The separation between the objective and eyepiece is `36cm` and the final image is formed at infinity. Determine the focal length of objective and eyepiece.A. `f_0 = 45 and f_e = -9 cm`B. `f_0 = 50 cm and f_e = 10 cm`C. `f_0 = 7.2 cm and f_e = 5 cm`D. `f_0 = 30 cm and f_e = 6 cm`.

An astronomical telescope has an angular magnification of magnitude `5

1.	An astronomical telescope has an angular magnification of magnitude `5` for distant object. The separation between the objective and eyepiece is `36cm` and the final image is formed at infinity. Determine the focal length of objective and eyepiece.A. `f_0 = 45 and f_e = -9 cm`B. `f_0 = 50 cm and f_e = 10 cm`C. `f_0 = 7.2 cm and f_e = 5 cm`D. `f_0 = 30 cm and f_e = 6 cm`.
Answer» Correct Answer - D Here, Angular magnification of telescope `= (f_0)/(f_e) = 5`, `:. f_0 = 5 f_e` …(i) Now, `f_0 + f_e = 36 cm` ….(ii) On solving (i) and (ii), we get `5 f_e + f_e = 36 cm` `f_e = 6 cm, f_0 = 30 cm`.

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