PARALLAX and Notes on using a Telescope

1. PARALLAX:

   To do quantitative work in optics one must understand parallax and how it may be eliminated. PARALLAX is defined as apparent motion of an object caused by actual motion of the observer.

   When the observer's eye is in position 1, objects 1 and 2 are in line and may appear to coincide. If the eye is moved to the left to position two, object 1 (i.e. O$_1$) appears to move to the left with respect to object 2, (i.e. O$_2$). If the eye moves to the right to position 3, object 1 (O$_1$) appears to move to the right with respect to object 2 (O$_2$).

   As object 1 moves toward position 2 along the dotted line, its apparent displacement with respect to object 2 caused by motion of the eye from 2 to 3 gets smaller until it vanishes when O$_1$ and O$_2$ coincide. When O$_1$ gets closer to the eye than O$_2$, the direction of its apparent displacement reverses for the same eye motion. In short, the object farthest from the eye apparently moves in the same direction as the eye. Try this with two fingers.

   Note that if O$_1$ is an image and O$_2$ a cross hair, the absence of parallax shows that the cross hairs are in the plane of the image.

2. Focusing a Telescope for Parallel Rays:
   

   
   The eyepiece E slides back and forth in the tube T and one should first adjust the eyepiece to give a clear image of the cross hairs. Then move the tube T back and forth in the barrel B until the image of a distant object, formed by the objective O, falls on the plane of the cross hairs. The test for this is the absence of parallax between the cross hairs and image.

   The rays from a distant object are nearly parallel. For viewing a distant object, use an open window if the window glass is not accurately plane. Otherwise poor image formation may result. You can check by trying it both ways. At night use a distant object in the hallway.

   The telescope, now focused for parallel rays, will stay so as long as the distance between O and C is unchanged. One may still adjust the eyepiece position to suit the observer.

3. Finding an Image in a Telescope:

   If you have trouble finding an image in a telescope, locate the image first with your unaided eye, and then pull the telescope in front of your eye, aligning it with your line of sight. With high magnification it is difficult to find the image in the telescope because the alignment must be nearly perfect before the image appears in the field of view. The eye has a rather large field of view so that the image will be visible over a range of positions.