The soap solution appears cloudy because soap micelles can scatter light. When a beam of light passes through a clear substance, such as water, the light rays travel in a straight line and do not disperse. However, when the light passes through a soap solution, the soap molecules arrange themselves into structures called micelles. These micelles have a hydrophobic (water-repelling) tail and a hydrophilic (water-attracting) head.
When light encounters these micelles, it interacts with them and gets scattered in different directions. This scattering of light is responsible for the cloudy appearance of the soap solution. The micelles act as tiny particles that scatter the light rays, causing them to be redirected in various directions. As a result, the light does not pass through the solution in a straight line, leading to a cloudy appearance.
Refracting light (option 1), diffracting light (option 3), and polarizing light (option 4) are not the primary reasons for the cloudiness of the soap solution. So the correct answer is option 2: soap micelles scatter light.