The Simple Astronomical Telescope Angular Magnification by Astronomical

The Simple Astronomical Telescope

Angular Magnification by Astronomical Telescope The angular magnification, M, (also sometimes called magnifying power) produced by an optical instrument is defined as

The Light From A Distant Object • • Remember that the light rays from any given point on a distant object arrive parallel at our eyes This is why the moon appears to stay in the same place in the sky as we travel on a train. However for us to see a distant object there must be an “angular distance” between the top of the object and its base • Notice that the rays from each point on the object are parallel to each other

eye Light rays from the top of the distant object Light rays from the base of the distant object α α α The angle α between any light rays coming from the top of the distant object and the light ray coming from the base of the object is the same at any point on the eye’ α is called the angle “subtended by the object” at the eye.

Here the eye has been replaced by the OBJECTIVE lens (the main “front” lens) of a telescope The light arriving parallel to the principle axis is focussed at F F focal plane Parallel light arriving from the top of the object is focussed below F on the focal plane.

The Telescope in Normal Operation Focal plane of the lens Focal length of eyepiece lens Light rays emerge parallel from the eyepiece lens In normal operation the eyepiece lens of the telescope is placed so that the principal focus of the objective lens is at the principal focus of the eyepiece lens Focal length of objective lens

o’ angle α is the angle subtended by the object with the unaided eye o’ represents rays from the top of the distant object angle β is the angle subtended at the eye using the telescope o’ β o’ The angles are exaggerated so we need to extend the eyepiece lens

For simplicity In the notes that follow we imagine two separate “point” objects at very large distance. They may be two stars A and B B α A Rays are arriving parallel at Earth from B Rays are arriving parallel at Earth from A There is a small angle α subtended at the eye between A and B

Light from object A (blue lines) meets at the principal focus of the objective lens. It then spreads out until it meets the eyepiece. The eyepiece is set at the focal length away from its principal focus. Parallel rays emerge from the eyepiece.

At the same time parallel rays from object B arrives at the objective at a small angle a to the axis. The light is focused onto the focal plane. It then passes through the eyepiece to emerge as parallel rays. The angle of these parallel rays is b to the parallel rays from A. The rays appear to come from an infinitely distant virtual image.

A simple expression for the magnification of the telescope = β/α α fo α h Using the small angle approximation fe β β