A polarized Light of intensity I0 is incident on an analyzer. What should the angle between the axis of polarization of the light and the transmission axis of the analyzer be to allow 38% of the total intensity to be transmitted?

The the angle between the axis of polarization of the light and the transmission axis of the analyzer is 52⁰.

Explanation:

Given;

I₀ as incident light intensity

The intensity of a linearly polarized light passing through a polarizer is given by Malus' law:

I = I₀Cos²θ

where;

I is the intensity after passing through the analyzer

θ is the the angle between the axis of polarization of the light and the transmission axis of the analyzer.

If 38% of the total intensity is transmitted, then I = 38% of I₀ = 0.38I₀

0.38I₀ = I₀Cos²θ

0.38 = Cos²θ

Cosθ = √0.38

Cosθ = 0.6164

θ = Cos⁻¹ (0.6164)

θ = 51.95° = 52⁰

Therefore, the angle between the axis of polarization of the light and the transmission axis of the analyzer to allow 38% of the total intensity to be transmitted is 52⁰.