Authors: Sheenah Ancheta, Monica Cecila Deleon, Krishna Lyn Delima, Matthew Steven Dinglasan, Mary Chris Go, Daniella Hernandez, Samantha Ruth Lahoz
Project under Optics course taken in University of the Philipines Diliman (2018).
Telescope design summary
The ray diagram below shows the workings of the constructed astronomical telescope. The telescope consists of two convex lenses: the objective lens and the eyepiece. The objective lens has a focal length of 33 cm while the eyepiece has a focal length of 19 cm.
It can be observed that the focal lens of the objective lens coincides with the focal length of the eyepiece lens at a point. That is to say that the length of the telescope remains constant at 52 cm throughout its use.
An aperture stop with a limiting diameter of 3 cm was added to the setup. It is a distance 23 cm away from the eyepiece and 29 cm away from the objective lens. We used this to limit the amount of light that could pass through and reach the imaging area. Without this, the image will be too bright and the observer cannot see the image well. The aperture stop also helped prevent chromatic aberrations due to its function of limiting light rays. It was made sure that the interior surfaces of the telescope, whether it be the material used to hold the aperture stop or the lenses, is not shiny or reflective as it would have contributed to the processing of the image.
Let us consider the collimated rays from a distant object. The objective lens forms a real, inverted, and reduced image of the object (as indicated by the red arrow). This image then acts as the object of the eyepiece. The final image of the object is inverted with respect to the original object being viewed. As expected of this kind of telescope, the final image of the object is magnified, inverted and formed at infinity. In this case, the magnification is expected to be 1.7 times larger than the original object.
Materials used for the building of the telescope
- Picnic can
- Cardboard
- 2x Magnifying lenses from (different focal lengths and diameter)
- Duct tape
- Cutter and scissors
3D Model of Telescope
- Objective lens: 33 cm (diameter = 9.9cm)
- Eyepiece lens: 19 cm (diameter = 2.5cm)
- Magnification : -(33/19) = -1.7x
- Total length of telescope: 52 cm
- Aperture stop
- Diameter: 3 mm
- Length : 23 cm (from eyepiece), 29 cm (from objective lens)
Table of images
| Object location | Image | Image location |
|---|---|---|
| Less than objective focal length (< 30 cm) | Inverted | Far beyond eyepiece |
| Small distances (50cm) | Inverted | Far beyond eyepiece |
| Medium distances (100cm) | Inverted | Near eyepiece (but a good enough image is produced when you look into the scope) |
| Large distances (> 100cm) | Inverted | Focused image can be seen when you look inside the scope |
When you look into the telescope, objects farther away are much clearer. The final image (virtual) produced when objects are at S_o ~ infinity (i.e. the light rays are almost parallel) is inside the telescope, but the rays transmitted into the eye will be nearly parallel as well. Moreover, the image formed from the objective lens at small object distances are far and beyond the position of eyepiece lens. When the objects are too close to the objective lens, a clear image can only be seen away from the eyepiece. Also, due to the construction of the telescope and the focal length of the objective, the images were seen clearly but with different colors scattering. This is because of color aberrations on the objective lens. This phenomenon is observed when different wavelengths pass through the lens and focus on different points. The telescope was not long enough to let the different wavelengths intersect at one point.
Verification of focal length
The focal lengths of the eyepiece and objective lenses were determined by flashing a light very far from the lens (~ 2m). An expected sharp image will be formed on the viewing screen and the distance between the lens and the viewing screen was then measured. This served as the focal length of each lens. The obtained values for this procedure led to inaccuracies due to the light not being in infinite distance.
Verification of magnification
To verify the magnification of our telescope, we took a picture of a far away object both with and without the telescope from the same distance. From the photos (shown below), the heights of the object and the magnified image were measured in pixels. On the first trial, the image was magnified 1.86x. We tried again on a farther object and got a magnification of 1.62x. These experimental values are still close to our theoretical magnification of 33/19 = 1.74x, both having a relative error of 6.9%, which, given the many sources of error in our experimental setup and telescope (e.g. quality of camera, positioning of telescope and smartphone, object distances, approximated focal lengths), is fairly acceptable.
Sample images from telescope
Keep of the grass sign as seen unmagnified (left) and magnified (right) with our telescope. Magnification: 1.86x:
White box as seen unmagnified (left) and magnified (right)
with our telescope. Magnification: 1.62x:
Recommendations
It is recommended to wrap the inside of the can with black paper to prevent reflection of the incoming light rays from the objective lens. Also, a shorter focal length should be used to improve the magnification of the telescope. To improve the image of the telescope, the telescope should be longer to prevent color aberrations or the presence of different colors in the image seen from the eyepiece.