Unpolarised light of intensity 32Wm-2 passes through the combination of three polaroids such that the pass axis of the last polaroid is perpendicular to that of the pass axis of first polaroid. If intensity of emerging light is 3Wm-2 , then the angle between pass axis of first two polaroids is ______º .
Show Hint
Remember Malus’s law: \( I = I_0cos^2θ\), where I0 is the initial intensity and θ is the angle between the polarizer’s axis and the polarization direction of the incident light. For unpolarized light, the initial intensity is halved after the first polarizer
To solve this problem, we need to use Malus's Law, which states that when unpolarized light passes through a polaroid, the intensity of the light is halved. When light passes through subsequent polaroids, the intensity can be described by \(I = I_0 \cos^2 \theta\), where \(I_0\) is the initial intensity, and \(\theta\) is the angle between the light’s polarization direction and the polaroid’s pass axis. Given:
Initial intensity: \(I_0 = 32 \, \text{Wm}^{-2}\)
Intensity after first polaroid: \(I_1 = \frac{I_0}{2} = 16 \, \text{Wm}^{-2}\)
Next, let \(\theta\) be the angle between the pass axes of the first and second polaroids. Using Malus's Law:
\(I_2 = I_1 \cos^2 \theta\)
\(I_2 = 16 \cos^2 \theta\)
The emergent light intensity \(I_3\) from the third polaroid with pass axis perpendicular to the first can be described as follows, since the angle between the second and third polaroid pass axes is \(90^\circ - \theta\):
\(I_3 = I_2 \cos^2 (90^\circ - \theta)\)
\(I_3 = 16 \cos^2 \theta \sin^2 \theta\)
We're given \(I_3 = 3 \, \text{Wm}^{-2}\). Therefore:
