Math
For the Pinhole Camera there is not a substantial amount of math, and it's not very hard, but you have to be very precise (all the way down to millimeters) because otherwise your whole box could be screwed up causing your pictures to be really bad. The focal length is the length from the pinhole to where the paper is put (on the base). The equation for figuring out the ratio between the diameter of the pinhole and the focal length is call f-stop. The equation is f-stop = focal length / diameter. I used a resource online, called Mr. Pinhole, and it said that an ideal f-stop is 349. By having my f-stop be 349, I found a pinhole that was .62 mm. I multiplied these two together to get my focal length, which came to be 216 mm. With these measurements, I had to decide how my box was going to be made, was the pinhole going on the top side or the bottom side of the lid, were my sides going to go on top of the base or on the side of it. The cardboard that we used had a thickness of 4.5 mm so if we didn't have a plan before with what goes where, we would have to remeasure and cut out a whole new base or sides. For my base and lid, I used the dimensions of 9 inches by 6 inches so that I would be able to use exactly half a piece of paper, which is 8.5 inches by 5.5 inches. This gave me just enough room to be able to put the paper in and take it out with ease.
I found that, for the most part, the optimal amount of time for a picture is about 1 minute and 30 seconds when taken outside. When it was cloudy outside, more time was needed since less light was coming through. Rather, when it was very sunny outside, less time was needed since more light was coming through. It was tricky at times when it was partially cloudy because the sun would get bright and then clouds would come, so you had to play around with the exact amount of time based around 1 minute and 30 seconds. When trying to take pictures inside, a substantially more amount of time was needed since it was not bright light from the sun but rather dimmer lights from lightbulbs.
I found that, for the most part, the optimal amount of time for a picture is about 1 minute and 30 seconds when taken outside. When it was cloudy outside, more time was needed since less light was coming through. Rather, when it was very sunny outside, less time was needed since more light was coming through. It was tricky at times when it was partially cloudy because the sun would get bright and then clouds would come, so you had to play around with the exact amount of time based around 1 minute and 30 seconds. When trying to take pictures inside, a substantially more amount of time was needed since it was not bright light from the sun but rather dimmer lights from lightbulbs.
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