What Is the Minimum Radius Needed to Paint on a Cube to Contain Light?

[firyace]

Lets say you got a glass cube and a small light source embedded at the exact center of the glass cube.
Now if you want to paint a circle on each face of the cube so that the light is prevented from leaving the cube, what is the minimum radius of the circle that you need to paint?

Let say each of the sides of the cube is 16.0cm.

Thanks!

 

[berkeman]

You need to show us your work so far in order for us to help you. Here's a starting point:

http://en.wikipedia.org/wiki/Total_internal_reflection

 

[kyle8921]

I would approach this question by considering the principles of light wave propagation and the behavior of light in different mediums. Light is a form of electromagnetic radiation that travels in a straight line until it interacts with an object or medium. When light enters a medium, such as glass, it can be refracted or bent due to the change in its speed.

In this scenario, the light source embedded at the center of the glass cube will emit light in all directions. As the light travels through the glass, it will be refracted and will continue to travel in a straight line until it reaches the boundaries of the cube. At these boundaries, the light will either be reflected or transmitted, depending on the angle of incidence and the properties of the material.

To prevent the light from leaving the cube, we need to ensure that the light rays are constantly being reflected or absorbed by the painted circles on each face of the cube. The minimum radius of the circle needed will depend on the angle of incidence and the thickness of the glass cube. In this case, the sides of the cube are 16.0 cm, so the minimum radius of the circle would also be 16.0 cm.

This is because if the radius is smaller than the sides of the cube, there is a possibility that some light rays will still be able to escape through the corners or edges of the cube. On the other hand, if the radius is larger than the sides of the cube, the painted circles may overlap and block the light source from emitting any light at all.

In conclusion, the minimum radius of the circle that needs to be painted on each face of the glass cube would be 16.0 cm, which is equal to the sides of the cube. This will ensure that all light rays are constantly being reflected or absorbed, preventing the light from leaving the cube.