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  4. The magnifying power of a telescope in its normal adjustment is 20. If the length of the telescope is 105 cm in this adjustment, the focal length of the objective lens is

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Q. The magnifying power of a telescope in its normal adjustment is 20. If the length of the telescope is 105 cm in this adjustment, the focal length of the objective lens is

MGIMS WardhaMGIMS Wardha 2014

Solution:

For normal adjustment, magnification is given by $ m=\frac{{{f}_{o}}}{{{f}_{e}}} $ and the length of the telescope tube is $ {{f}_{0}}+{{f}_{e}} $ . Let the focal length of objective and eye lenses are $ {{f}_{o}} $ and $ {{f}_{e}} $ respectively. Therefore, magnification $ m=\frac{{{f}_{o}}}{{{f}_{e}}}, $ $ 20=\frac{{{f}_{o}}}{{{f}_{e}}}\Rightarrow {{f}_{o}}=20{{f}_{e}} $ And $ {{f}_{o}}+{{f}_{e}}=105, $ On solving, $ {{f}_{o}}=100 $ cm and $ {{f}_{e}}~=5cm $ .