Question

(a) Draw a labelled ray diagram to obtain the real image formed by an astronomical telescope in normal adjustment position. Define its magnifying power.

(b) You are given three lenses of power 0.5 D, 4 D and 10 D to design a telescope.

(i) Which lenses should he used as objective and eyepiece ? Justify your answer.

ii) Why is the aperture of the objective preferred to be large?

Solution

a) The image formed by an astronomical telescope in normal adjustment position is given below,

In normal adjustment, the image is formed at infinity.
Magnification power is defined as the angle subtended at the eye, by the final image, to the angle subtended at the eye, by the object directly, when the final image and the object both are at infinity.

Mathematically, it is given by
Magnification, m =

straight beta over straight alpha

Since

straight alpha space and space straight beta

are very small,

straight beta space equals space tan space straight beta straight alpha space equals space tan space straight alpha rightwards double arrow straight m equals space fraction numerator tan space straight beta over denominator tan space straight alpha end fraction

b) Given, three lenses of power 0.5 D, 0.4 D and 10 D.
i) The formula for magnification, M =

straight f subscript straight o over straight f subscript straight e equals P subscript e over P subscript o

Therefore, an objective with power = 0.5 D and eyepiece of power 10 D should be used.
This choice would give a higher magnification.
ii) The aperture is preferred to be large so that the telescope can collect maximum amount of light coming from the distant object.

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