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Hi! I just had a quick question on the topic of optics. I did an experiment wher I shone a flashlight's beam through several sized holes at an object. I noticed that the larger the light source, the smaller the object's umbra was and the larger the penumbra was. Why was that? And for a smaller source of light, the object's umbra was larger and the penumbra was smaller. Why was that? Thanks!
Answer 1:

I was just thinking about shadows the other day. If you look at photographs taken with a flash, they often have really harsh, sharp edged shadows. But,if the photographer decides to get the light from other sources, the shadows have a nice large penumbra, sometimes so much that the shadows aren't visible. In these cases, the shadows produced by the flash are from a small light source, and the shadows that have large penumbras are produced by very large light sources.

So why does a large light source make a larger penumbra? Let's try a"thought" experiment. Let's take one object, and two very small light sources that are separated. If we just turn on one light , the object's shadows should be well defined- no penumbra and all umbra. Now, if we turn on the second light, there will be two shadows, but the dark parts won't be as dark as with one light. Why is this? One of the lights is putting light into the other light's shadow. In a way, we've made a well-defined penumbranow.

So how does this all apply to your original question? You can think of the large light source as have a bunch of small lights at the opening. The more spread out the lights are, the more spread out the penumbra is and the smaller the umbra is, just like our thought experiment. If you keep shrinking the distance between the light sources, eventually you end up with one tiny light source again, and the shadow should be all umbra.

Another way to look at this is with ray optics. You can look up information about ray optics in many textbooks on physics. Ask your teacher if you need help finding information. Once you've looked at ray optics, you can figure out how bright any point is by seeing how much of the light source that point "sees." Just as an example, in the umbra, those points can't see the light, so that's why it's dark.


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