An unpolarized light beam is incident on the polarizer of a polarization experiment and the intensity of light beam emerging from the analyzer is measured as 100 Lumens. Now, if the analyzer is rotated around the horizontal axis (direction of light) by 30° in clockwise direction, the intensity of emerging light will be ______ Lumens.

We have an unpolarized light beam passing through a polarizer and an analyzer. The intensity emerging from the analyzer is initially measured as 100 Lumens.

When unpolarized light of intensity $$I_0$$ passes through a polarizer, the transmitted intensity becomes $$\frac{I_0}{2}$$. When this polarized light then passes through the analyzer at an angle $$\theta$$ to the polarizer, by Malus's law, the transmitted intensity is $$I = \frac{I_0}{2}\cos^2\theta$$.

Initially, the polarizer and analyzer are aligned ($$\theta = 0°$$), so $$100 = \frac{I_0}{2}\cos^2 0° = \frac{I_0}{2}$$.

Now the analyzer is rotated by 30°. The new intensity is $$I' = \frac{I_0}{2}\cos^2 30°$$.

We know $$\cos 30° = \frac{\sqrt{3}}{2}$$, so $$\cos^2 30° = \frac{3}{4}$$.

$$I' = \frac{I_0}{2} \times \frac{3}{4} = 100 \times \frac{3}{4} = 75$$ Lumens.

So, the answer is $$75$$.