Question

Answer the following question in detail.

Obtain the expressions for magnifying power and the length of an astronomical telescope under normal adjustments.

Answer 1

1. For telescopes, α is the visual angle of the object from its own position, which is practically at infinity.
2. 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
3. The parallax at the cross wires can be avoided by using the telescopes in normal adjustments.
4. The objective of focal length f_o focusses the parallel incident beam at a distance f_o from the objective giving an inverted image AB.
5. 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.
6. 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"`
7. Length of the telescope for normal adjustment is, L = f_o + f_e.