A

Step 1: Given that the intensity of light emerging from the analyzer is initially 100 Lumens.
Step 2: When a polarizer is positioned in front of unpolarized light, the intensity of the light that passes through is given by Malus's Law:
\( I = I_0 \cos^2(\theta) \)
where \( I_0 \) is the intensity of the incident light and \( \theta \) is the angle between the light's polarization direction and the analyzer.
Step 3: If the angle is initially 0° (perfect alignment), the intensity is 100 Lumens.
Step 4: After rotating the analyzer by 30°, the new intensity can be calculated as:
\( I = 100 \cos^2(30°)
= 100 \times \left(\frac{\sqrt{3}}{2}\right)^2
= 100 \times \frac{3}{4}
= 75 Lumens.
Therefore, the final intensity of the emerging light will be 75 Lumens.