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Question
Answer the following question in detail.
Obtain the expressions for magnifying power and the length of an astronomical telescope under normal adjustments.
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Solution
- For telescopes, α is the visual angle of the object from its own position, which is practically at infinity.
- The visual angle of the final image is β and its position can be adjusted to be at D. However, under normal adjustments, the final image is also at infinity making a greater visual angle than that of the object.
Telescope - The parallax at the cross wires can be avoided by using the telescopes in normal adjustments.
- The objective of focal length fo focusses the parallel incident beam at a distance fo from the objective giving an inverted image AB.
- For normal adjustment, the intermediate image AB forms at the focus of the eye lens. Rays refracted beyond the eye lens form a parallel beam inclined at an angle β with the principal axis.
- Angular magnification or magnifying power for telescope is given by,
M = `β/α≈(tan(β))/(tan(α))=("BA/P"_"e""B")/("BA/P"_"o""B")="f"_"o"/"f"_"e"` - Length of the telescope for normal adjustment is, L = fo + fe.
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