Working Principle of an Astronomical Telescope
The telescope uses a lens as an objective, and is called a refracting telescope or refractor. The
objective lens forms a real, reduced image I of the object. This image serves as the object for the
eyepiece lens, which forms an enlarged, virtual image of I. Objects that are viewed with a telescope
are usually far away from the instrument that the first image I is formed very nearly at the second
focal point of the objective lens. If the final image I' formed by the eyepiece is at infinity (for most
comfortable viewing by a normal eye), the first image must also be at the first focal point of the
eyepiece. The distance between the objective and eyepiece, which is the length of the telescope, is
therefore the sum of the focal lengths of the objective and eyepiece, f1+f2.
The angular magnification M of a telescope is defined as the ratio of the angle subtended at the eye
by the final image I' to the angle subtended at the eye by the object. We can express this ratio in
terms of the focal lengths of the objective and eyepiece. The object (not shown) subtends an angle θ
at the objective and would subtend essentially the same angle at the eye. Also, since the observer's
eye is placed just to the right of the focal point F2', the angle subtended at the eye by the final image
is very nearly equal to the angle θ'. As bd is parallel to the optic axis, the distances ab and cd are
equal to each other and also to the height y' of the real image I. Because the angles θ and θ' are
small, they may be approximated by their tangents. From the right triangles F1ab
and F2cd,
θ = -y'/f1
θ' = y'/f2
And the angular magnification M is
M = θ' / θ = (y'/f2)/(-y'/f1) = - f1/f2
The angular magnification M of a telescope is equal to the ratio of the focal length of the objective to
that of the eyepiece. The negative sign shows that the final image is inverted. This equation shows
that to achieve good angular magnification, a telescope should have a long objective focal length f1.
