QJEEM18Ph0e68: JEE Main 2018 Physics - Class 12 JEEM18Ph0e68 Solution: Unpolarized light of intensity I is incident on a system of two …

As intensity of emergent beam is reduced to half after passing through two polarisers. It means angle between A and B is 0$${}^{\circ }$$.

Now, on placing polariser C between A and B.

Intensity after passing through A is $$I_A=\frac{I}{2}$$.

Let $$\theta$$ be the angle between A and C. Intensity of light after passing through C is given by

$$I_C=\frac{I}{2}{\cos }^2\theta$$

Intensity of light after passing through polariser B is $$\frac{I}{3}$$.

Angle between C and B is also $$\theta$$ as A is parallel to B.

So, $$\frac{I}{3}=I_C{\cos }^2\theta =\frac{I}{2}{\cos }^2\theta .{\cos }^2\theta$$

$${\cos }^4\theta =\frac{2}{3}\Rightarrow \cos \theta ={\left(\frac{2}{3}\right)}^{1/4}$$