The Pinhole Camera
R. Shankar, The Institute of Mathematical Sciences, Chennai
Vikram, a young tusker in Mudumalai sanctury, and his friend Lakshmi, a mahout's daughter, were sitting under a tree one lazy Sunday afternoon.  "I took a very nice family with two little girls for the forest ride yesterday" said Vikram, "they had gone to Kanyakumari to see the eclipse. The father had not been able to go so the little girls were telling him all about it". 
The total annular eclipse on 15th January, 2010 had occurred just a week before. Vikram and Lakshmi had seen it together in Mudumalai. Lakshmi had managed to get a welder's glass for Vikram. Though the glass was big, Vikram's head was of course even bigger. So Lakshmi had closed one of his eyes with a bedsheet and had put the glass in front of his other eye.  But this was not very comfortable, also elephants cannot turn up their heads, so Vikram could not really see it very well.
"They said that that there was a group of students from a place called Nanded, who had used some camera to make many pictures of the sun on the ground". "Don't be silly !" retorted Lakshmi, "Cameras used to make pictures on film and paper, nowadays they make it on computers but they cannot make pictures on the ground". "Well, I did not really understand what they said. They called it a camera but the way they were talking about it, it seemed to be just a piece of paper with some holes in it".  "Oh ! A pinhole camera !", exclaimed Lakshmi, "Our teacher once showed one to us, but I never thought of using it to see the eclipse. Come, I'll show you".
Vikram lifted his leg and bent his knee, Lakshmi used it as a step, clambered on to his back and they went to Lakshmi's house in the elephant camp. Lakshmi took a pice of stiff paper (an old greeting card) and made a nice small circular hole in it using her pencil. She then placed a table lamp on the table and pulled the curtains to darken the room. All except one window outside which Vikram was standing and looking on with great interest.
She put on the lamp and held the paper between the bulb and the wall. The shadow of the card fell on the wall.  "That's just a shadow, why do you call it a camera ?" "Arrey ! Be a little patient and just watch" Lakshmi adjusted the angle of the paper and the light going through the hole made a bright spot on the wall. She then adjusted the distance of the paper from the bulb and suddenly a picture of the wire inside the bulb appeared on the wall.
"Hey ! That's cool !", Vikram had clearly been influenced by the language of some of the tourists, but he was really excited."That is like a camera ! I can see the wire ! It's beautiful !  "Isn't it ?" smiled Lakshmi, quite pleased by the effect, "This is what my teacher had shown us. If it makes a picture of the bulb, then I suppose it will also make a picture of the sun".
They watched for a few minutes. "But they said that there were many pictures of the sun, try making two holes and let us see what happens ?" So Lakshmi made another hole a little distance away from the first and adjusted the position of the card again. Sure enough, two pictures of the filament appeared on the wall. "Ha ! it works ! Let me make more holes". But in her excitement the hole became a little uneven. It was wide on one side and narrow on the other. "Oh dear, I've messed it up.
I'll patch it up and do it again". "But let us see anyway", said Vikram, "It may show us a crooked wire". So Lakshmi held it up again. Three pictures of the wire appeared but all were perfect. "Strange ! it does not seem to make difference to the picture" said a puzzled Lakshmi, "let me try a different shape". She got a blade and cut out a neat triangle. The picture of the wire was again perfect.
"Take the paper very close to the wall" said Vikram, "surely then we must see a triangle". That turned out to be true. When the paper was very close, they could see a triangle but no wire.
They tried different shapes and the result remained the same. When the paper was very close to the wall, they could see the shape of the hole.  When it was further away and at the right position they could see the picture of the bulb filament. When there were many holes, they could see many filaments -- there were as many filaments as holes.
"Why does the shape of the hole not matter when we see the wire" wondered Vikram. "Why don't we see the wire when we see the shape of the hole ?" echoed Lakshmi. "Why do we see the picture of the bulb wire at all ?" They pondered about this puzzle for some time. Then they gave up. "I will show this to my teacher and ask her" said Lakshmi. 
Then she made many pretty patterns of holes on pieces of paper and both of them spent a nice couple of hours looking at the pictures of the patterns on the wall made up of many small pictures of the bulb wire.
BOX: The size of the pin-hole
What should be the size of the pin-hole, to get the clearest picture?  This depends on whether you are watching an eclipse or whether you are actually trying to take photographs. For photography, the best pin-hole is round, on a very thin piece of material. For projecting the image of the Sun on the ground, it is not so critical. Even a punching-machine (used to make holes for filing papers) will do. If you are watching the Sun then the light has a wavelength (in the visible region) of about l=550 nm (1nm = 1/100,000,000 m or 10-9 m). For a distance f from the pin-hole to the ground, the best size of hole turns out to be about d=2\sqrt{fl}.  For f=few m, this works out to be d=2mm. If you are holding the pin-hole just a few cm above the ground, the hole had better be finer than 1 mm.  During the eclipse, small gaps in leafy trees about 2-3 m above ground act as natural pin-hole cameras and project bright crescent images of the Sun on the ground (see picture). Especially when eclipses are during mid-afternoon so that the Sun is high in the sky, this causes a spectacular effect.