Download The angles are exaggerated so we need to

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Here the eye has been replaced by the OBJECTIVE lens (the main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’
Rays from the top of the
object (o’) appear at infinity.
This is a virtual image
The angles are
exaggerated so we
need to extend the
eyepiece lens
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.
h
h
 , 
fo
fe
h  f o   f e
 fo

 fe
fo
M 
fe
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.
A simple expression for the magnification of the
telescope
= β/α
α
fo
fe
β
α
h
h
tan  
fo
β
h
tan  
fe
Using the small angle approximation
h
h
 , 
fo
fe
Concave mirriors
Parallel rays are brought to a principle focus by a concave mirror
The Cassegrain arrangement of
mirrors
to eyepiece
The Newtonian arrangement