PASCO OS-8500 INTRODUCTORY OPTICS SYSTEM - Manual (Page 54)

Introductory Optics System 012-02744K
®
48
Figure 21.1 shows the setup for a simple telescope. The objective lens, L
1
, creates a real, inverted
image. (You can barely see this image in the diagram. It's very small, just inside the focal point of
lens L
2
.) If the object is sufficiently far away, this image will be located approximately at f
1
, the
focal point of L
1
. The eyepiece, L
2
, then acts as a magnifier, creating a magnified, virtual image
which can be viewed by the observer. For maximum magnification, L
2
is positioned so the virtual
image is just slightly closer than its focal point, f
2
. Therefore, the distance between the objective
lens and the eyepiece of a telescope, when viewing distant objects, is approximately f
1
+ f
2
.
The angular magnification (see Experiment 20: The Magnifier) for a telescope can be approxi-
mated by assuming the lenses are exactly f
1
+ f
2
apart, as shown in Figure 21.2. The height of the
object as seen with the naked eye is proportional to the angle q
1
in the lower diagram. If the
distance from the object to the telescope is large—much larger than is shown in the diagram—
θ
1
=
θ
1
´, to a good approximation. The ray shown in the upper diagram passes through the focal
point of the objective lens, comes out parallel to the optical axis of the telescope, and is therefore
refracted by the eyepiece through the focal point of the eyepiece. The angle
θ
2
is therefore propor-
tional to h
i
, the height of the image seen by the observer.
Procedure
➀ Using Figure 21.2, calculate tan θ
1
and tan
θ
2
as a function of the height of the image, h
i
, and the
focal lengths of the two lenses, f
1
and f
2
.
tan
θ
1
= tan
θ
1
´ = ______________________________________________.
tan
θ
2
= ________________________________________________.
Assume that
θ
1
and
θ
2
are very small, and therefore equal to tan
θ
1
and tan
θ
2
, respectively.
➁ Calculate the angular magnification of the telescope.
Angular Magnification =
θ
2
/
θ
1
= _______________________________________ ______.
Set up a telescope using the 75 mm and 150 mm focal length lenses; the distance between the
lenses should be approximately 225 mm. Using the 75 mm lens as the eyepiece, look at some
reasonably distant object. Adjust the distance between the lenses as needed to bring the object into
sharp focus.
To measure the magnification, look with one eye through the telescope, and with the other eye
look directly at the object. Compare the size of the two images. (If a meter stick is used as the
object, fairly accurate measurements of magnification can be made.)
➂ What is the magnification of the telescope when using the 75 mm lens as the eyepiece?
________________________________________________________________________
________________________________________________________________________.
➃ What is the magnification of the telescope when using the 150 mm lens as the eyepiece and the 75
mm lens as the objective lens?
________________________________________________________________________
________________________________________________________________________.
➄ Are your answers to questions 3 and 4 in keeping with your answer to question 2?
________________________________________________________________________
________________________________________________________________________.