Final answer:
The physics problem requires understanding how light intensity changes based on an angle when applying Malus's Law. If 25% of the initial intensity is left, then I = 0.25 Io and this equation is used to determine the angle that results in this intensity level.
Step-by-step explanation:
The question involves calculating the intensity of a wave and is a physics-related problem, typically at the high school level. When the intensity of light is reduced by a certain percentage, the resulting intensity can be found by multiplying the original intensity (Io) by the decimal equivalent of the remaining percentage. For example, when the intensity is reduced by 90.0%, the resulting intensity would be at 10.0% or 0.100 times its original value.
Using the equation I = Io cos², you can solve for the angle, assuming that the intensity (I) is the percentage of the original intensity that is left after passing through a medium or after an event that diminishes it. If I = 0.100 Io, you are looking for the cosine squared of the angle that, when multiplied by the initial intensity, gives you the current intensity. Similarly, if you're given that 25% of the initial intensity remains, you would say I = 0.25 Io and use the same formula to solve for the angle.
For instance, if the problem involves an intensity being reduced to 25%, you would set up the equation as I = Io cos² or 0.25 Io = Io cos² and then solve for the angle from there. This equation often arises in the context of Malus's Law, which describes the intensity of polarized light after passing through a polarizing filter at a certain angle.