A simple solar image projection setup can be made using a hard plastic ball.
The best way to make an image of the Sun is to project its image using either using a lens or a mirror or a telescope or a pair of binoculars.
The size of the projected image depends on the focal length of the objective (lens or mirror) and the focal length of the eyepiece if telescope or binoculars are used.
Tip the longer the focal length of an objective bigger will be the image. And the bigger the diameter of the objective more light it will collect and the brighter will be the image.
Trap for the same set up of telescope and eyepiece combination larger the size of the image fainter it will be.
Astronomers use a term called plate scale to get an estimate of the size of the image. This term has come from the photographic era. It is a relation between the focal plane, s, to its angular size in the sky.
Plate scale, P, relates the size of the image in the focal plane, s, to the angular size of the object being imaged. Here s is directly related to the focal length of the objective and is measure in radians.
Astronomers usually refer to the plate scale in units of arcseconds per mm. As shown in the example problems, the plate scale is then given by
p = 206265 / f, where f is in mm.
For example 1: a normal lens in a camera has a focal length of 50 mm
The plate scale is 206265/50 = 4125.3 seconds of arc per mm
or 4125.3 / 3600 = 1.146 degrees per millimeter
We know that the angular diameter of the Sun is ~0.5 deg (half a degree).
Therefore, the size of the Sun’s image will be 1.146 x 0.5 = 0.573 or a little over half a millimeter.
Example 2: now let us say that we want the Sun image to be 100 mm.
That is 100 mm = > 30′ or 1800″ of arc
That is the plate scale here will be 1800/100 = 18 sec. arc per mm,
For this, we need focal length ‘f’ to be 206265/18 = 11459.16 mm
or 1145.916 cm, or 11.45916 meters. Or we need the focal length to be nearly 11.5 meter, which is a very long focal length.
Eyepiece Projection
Using an eyepiece one can project the image of the Sun (or for that matter any object).
The effective focal length of the = Telescope Focal Length x ( y ÷ x )
Where x and y are determined from the formula:
(1/F) = (1/y + 1/x); where f is the focal length of the eyepiece.
Try this once you have made an image, say that of the Sun, then measure its diameter in millimeters and calculate the effective focal length of the system.
Some examples of projecting the Sun
This telescope is made using a lens from a broken binocular. A microphone stand with a laboratory clamp is used for holding the telescope. Note the cardboard sheet fixed to the lens holder so that direct sunlight does not fall on the screen.
In this example, the telescope is mounted on a stand. This telescope also has a 45 degree flat mirror for directing the image of the Sun so that screen can be kept in the natural shadow area. In the second image, we used a shoebox. We cut a square aperture and placed a white sheet inside the box. This improves the contrast of the image.
In case you are using an eyepiece fixed in a plastic casing the be careful. The strong concentrated sunlight can actually melt the plastic as seen below.
You can see from this example that a very large image of the Sun can be projected inside a room.
This method of projecting the Sun has one disadvantage and that is as the Sum moves in the sky we need to change the direction of the telescope.
To overcome this issue one can keep the telescope fixed at one location and reflect the sunlight to the primary optics of the telescope. There are basically two types of mounts Heliostats and Coelostats. For a very good summary of these three mounts see this paper by A A Mills.
A Heliostat has a plane mirror which is moved so that it reflects the sunlight to a fix point. The issue with his type of mount is that as the sun moves across the sky the image rotates. It is like an altazimuth mount. These are mostly used is solar-thermal power station. A large number of heliostats, operating together, are used for directing the sunlight to a fix point.
Heliostat projection – the Sun image rotates
A Coelostats are like equatorial mounts. A plane mirror is mounted on a polar axis. The axis is rotated is such a way that the sunlight is reflected to another mirror. This mirror can be turned to direct the sunlight to a fix telescope. Here the image of the sun does not rotate.
Coelostat projection – the Sun Image does not rotate
DIYA 