91Ó°ÊÓ

Intensity: The power transferred per unit area is the intensity of radiant energy in physics, where the area is measured on a plane perpendicular to the energy's propagation direction.

Considering the given information,

Intensity of transmitted wave is half of the incident wave.

Apply the formula,

The intensity of the transmitted wave is proportional to the intensity of the incident wave:

\(I = {I_o}{\cos ^2}\theta \)

Here,

The intensity of transmitted light is denoted by\(I\).

The incident wave's intensity is denoted by\({I_o}\).

The angle between the direction of polarised light and the axis of the polarizing filter is denoted by the symbol\(\theta \).

If the incident wave's intensity is\({I_o}\), the transmitted wave's intensity should be\({{\rm{I}}_{\rm{o}}}{\rm{/2}}\), according to the question.

The incident wave's intensity is proportional to the transmitted wave's intensity.

\(I = {I_o}{\cos ^2}\theta \)

Putting the values,

\(\begin{aligned}\dfrac{{{I_o}}}{2} &= {I_o}{\cos ^2}\theta \\\dfrac{1}{2} &= {\cos ^2}\theta \\\theta &= {45^ \circ }\end{aligned}\)

Therefore, the requiredangle between the direction of polarized light and the axis of polarizing filter is\({45^ \circ }\).