To measure the diameter of the sun with the help of a simple experiment.
1. One bottle with 2 liter capacity.
2. A small mirror made of thermoplastic (less than 0.5cms * 0.5cms).
3. A stand to hold the bottle in place. (Books or even bricks can be used to hold it firmly).
4. Glue -hot enough to paste the mirror to the bottle.
5. Water to fill the bottle.
6. Hard white viewing board preferably a poster board.
7. Stopwatch and a pencil.
1. Make a stand to hold the bottle firm enough so that it doesn’t roll off.
2. Paste the mirror somewhere at the centre along the length of the bottle.
3. Fill up the bottle with water
4. Now place the bottle with its stand outside such that the mirror faces the sun, directly. Take the viewing screen, stopwatch and pencil along with you.
5. Hold the viewing screen a few meters away from the mirror. You may need a partner to hold the screen on place. Rotate the bottle such that you get an image of the sun on your viewing screen.
6. The image formed on the screen is best only when the mirror is perpendicular to sun’s rays and the screen is somewhat parallel to the mirror. This set up is easy to configure when the sun is closer to the horizon. Observe the image. Mark it using a pencil on the poster board.
7. Use the stopwatch to keep track of the time as the image of the sun moves completely out of the first image (circle). Stop the time and trace the second image. Repeat this several times. (At least five measurements, This experiment will take a whole day or two.)
8. Now alter the size of the image by varying the distance of the screen from the mirror. Repeat as above i.e. by marking the images on the poster board and by keeping track of the time.
The mirror on the bottle is forming images of the sun on the screen. As a result we get two similar triangles. One of them is an isosceles triangle. The base of the isosceles triangle is sun’s diameter here with its sides as the rays coming from each sides of the sun’s diameter towards the mirror. The other image formed on the screen is similar to the one on the mirror with its base as the sun’s diameter while sides formed out of rays coming out of the two ends of the diameter. As these triangles are similar therefore the angular diameter of the image formed on the screen should be equal to the angular diameter of the sun up above. We calculate the sun’s angular diameter as follows:
The rotation of earth causes the image to shift continues across the screen. The earth completes one rotation i.e. 360 degrees in 24 hours. So by unitary method we get that it rotates by 15 degrees every hour i.e. 0.25 degrees every minute. From observation we saw that it takes 2 minutes for the sun’s image to move by “one sun diameter”. This would be the same for larger and smaller images as it is a measure for earth’s rotation which is a constant. The following formula can be used:
15 degrees/60 minutes= X degrees/2 minutes
X= sun’s angular diameter.