I recently came across a question in which we had to find the force acting on a cube due to light beam directed along its body diagonal with a certain intensity. I am having trouble visualising the situation and have no idea what to do. In which direction will such a force be directed if the light is completely reflected? Can we actually break the light into components and calculate force on individual faces? Would someone please help me out?
Since this is a homework-like question, I won't solve it for you. However, I will give you some pointers.
- Draw a picture and calculate the angle between the surface normals and the body diagonal.
- The total reflection indicates that you have to use "angle of incidence = angle of reflection" (Snell's law).
- By symmetry you can deduce the direction of the total (=summed) momentum. Use this information: Consider a single ray and calculate the change of momentum in the direction of the final direction. This involves a projection onto this direction.
- We can definitely break up the calculation into individual surface. However, by using step 3 it becomes clear that we only have to consider the "cross section": If the length of one side of the cube is $a$, which surface area "sees" the incoming light?