Final answer:
The intensity of the light emerging from the polarizer is I0/4
Step-by-step explanation:
When unpolarized light passes through a polarizing filter, its intensity is reduced by a factor of 2. In this case, one beam is unpolarized and the other beam is polarized at an angle of 30.0 degrees to the polarizing axis of the polarizer. The intensity of the unpolarized beam after passing through the polarizer is I0/2. The intensity of the polarized beam after passing through the polarizer is I0/2 * cos^2(30.0 degrees), which simplifies to I0/4.